Well, it matters greatly. Let's think of fiber in terms of Human Hair (which, technically, can be considered a fiber..in a creepy, yet very wrong sense.).
Depending on your race, genetic disposition, and how your hair is cared for, it has different properties and textures. Caucasian hair, for the most part, can be curly or straight, but most of the time, has an even texture that's fairly easy to manipulate with a little product or tools. African Hair tends to be highly coarse. This means it can be corded, braided, and twisted with ease because the hair has a "springy" quality known as "Memory". Asian hair is, for the most part, stick straight and slick. Not a lot can be done with it, but with accessories and creative cutting, can be put together in an array of styles.
If you think of Yarn Fibers in these terms, it may be a little more understandable as to why pattern makers and knitter/crocheters alike use certain fibers for certain applications. For this lecture, I am lumping Fibers into 3 basic categories: Animal, Plant, & Man-Made
Animal Fiber: Animal fiber is the hair or fur from critters. In no certain order here are some that are popular and/or kinda odd.
Sheep
Alpaca (a type of Llama)
Angora (type of both goat and rabbit)
Merino (Goat)
Cashmere (Goat)
Bison (No, really)
Dog (couldn't make that up!)
In relation to human hair, Animal Fiber is like Caucasian Hair. It has texture and can be manipulated if you apply heat. If you "bump-it", you get volume or what is called "Felting" when you take an item made with an animal fiber and agitate the living ba-cheese-us out of it in hot, soapy water. Then again, African Hair "felts" also, in which is called "Dread Locks". But that's for another discussion on another site.
Animal Fibers are recommended for use in Garments for their softness and moisture resisting properties and for felting projects. What causes felting is the "barbs" that all animal (and human) hair has on each strand. If you watch Shampoo commercials, you will notice this. When hair is stripped of it's natural oils (via soap) and is viggoriously rubbed against itself (via aggitation..this is why hair tangles, btw, when you rub your head with a towel) those barbs link together like velcro (thus, felting).
Non-Animal fibers lack these barbs. Yeah, Cotton shrinks when you wash it a first time, but it doesn't link together. It just gets small and softens...which brings me too...
Plant Fiber: Plant Fiber are fibers that come from natural and/or organic resources. Plant fiber is the preferred choice of fiber for Vegan knitter/crocheters, or people who are trying to "go green". They may also be seen knitting or crocheting with Bamboo, Rosewood, or other wooden crafting tools. Here are the plant fiber yarns I know of thus far...
Cotton
Bamboo (you read that right)
Soy
Raffia
Hemp (heck yeah!)
Linen
Flax
Twine
In Human Hair terms, I would consider Plant Fibers to be the Asian Hair of the fiber kingdom. It's slick, it has no memory, but with the right tools, can make some really great styles.
Plant fibers are best for things such as summer garments, bags, and home items. Plant fibers retain little heat and offer killer liquid absorption. Both are excellent properties to have during the summer when you want a cute little top to wear, but animal & man-made fibers are just too warm. The durability of plant based yarn increase dramatically when it is knitted, crocheted, or even woven. This is why designers prefer these fibers for such things as purses, wash-clothes, rugs, and even rope. For example, cotton yarn in itself is fragile and easy to break if you pull on it just right. But once you use it in a seed stitch, or double crochet it, it will be one of the best dish-clothes you ever had! Also, plant fibers have no stretch or memory. Both a blessing and a curse. If you mess up, you're kind of boned. You can't just throw it on a Niddy Noddy, wet it, and hope for the best, but if you are making one of those super cool baby sling thinggers, then a good quality plant based yarn is going to be sweet! If you used a cheaper acrylic, it's going to stretch like crazy and then you will be carrying your child at your shins. As entertaining as the thought is, using your baby as an attached hacky sack is WRONG!
Man-Made Fiber: There is absolutely nothing wrong with using the cheap ol' stand-by of Acrylic Yarn. Now breath and make this your mantra when you just HAVE to knit/crochet something and all you have is $5 to your name and enough gas to get you to Craft Warehouse and back home. Here are the examples of Man-Made Fiber
Acrylic
Nylon
Plastic Bags (oh my, yes)
Chenille
Chitlin
note: for the record, Chitlin is technically an animal fiber being it is made from crab shells, but it is created chemically into a soft yarn. I've bought sock yarn made from it. It's pretty sweet. Also, does not hold the properties of Animal yarn. DOES NOT FELT.
Notice how I capitalized "Does Not Felt". Man-Made fibers are the African Hair of fiber. No matter how you treat it, manipulate it, or play with it, it will never felt or have ALL of the same properties of Animal Fiber. Case in point. Let's say 2 people make sweaters from the same pattern. Both use worsted weight yarn but one is using 100% Merino Wool, the other is using 100% Acrylic yarn. The Merino is going to have far better drape and feel to the sweater than the Acrylic which, no matter how the person steams it, blocks it, or incorporates a few tactful short row shaping here and there, their sweater will just look cheap and uncomfortable.
Man-Made fibers are used more or less for items in the "Others" category. Usually afghans, Slipper Socks, Hats, Mittens, Decor, or What-Ever in general. BUT!!!...THERE IS EXCEPTION TO THIS!!!
There are some Man-Made fibers that are made in a "soft" format. To be very specific, yarn examples such as Caron Simply Soft or Vanna's Choice make GREAT "Garment" yarns if you are looking to make a sweater on the cheap. My only warning is that they may not be as warm as animal fiber, and not as moisture wicking as plant-based fiber. When wearing a man-made fiber garment, I do suggest wearing an under garment.
Blends: Now, let's say you want to make a cute sweater for your Brother's 3 year old boy. You want the sweater to be soft and warm for the upcoming winter season, but kids are HARSH on clothing so you want some stellar durability let alone want it to be washable, since your Sister-in-Law has her hands too full with the darling kiddo to hand-wash a hand-knit sweater. Which yarn do you go for? A blend!
Blends are that math-equation you peeked over Marty McMathelson's shoulder during the big Algebra quiz. The answer to your scenario, as stated above: You want yarn that's X% animal, Y% Man Made. The more animal, the softer and warmer. The more man-made, the more washable and durable. The same goes for with plant fiber...If you want to make a really cute Short-Sleeve Kimono Wrap style top, but won't shrink completely in the wash, or become totally disfigured in the wash, get yarn that's X%Plant, Y% Man made. The more Plant, the cooler and more liquid wicking. The more Man-made, the more washable and shape retaining.
Blending fills in the gaps and solves the problems you have with 100% of something may have cons too. You can even find blends of like animal to animal, or like plant to plant, or even like man-made to man-made because each different type of something has it's own goodies to it!
I hope this has been helpful to you, my readers. Fiber Knowledge is essential if you ever want to substitute one yarn for another in a project. I'd hate to see you use an el cheapo acrylic yarn instead of the suggested cotton for the drum bag, then have your clutch size strap hang to your knees because you didn't know how bad acrylic stretches.
If you have further questions regarding fiber, please comment below and I will try my best to answer.