Do you know how at the beginning of James Bond films the point of view is from inside the barrel of a gun, complete with its swirling rifling? It’s the swirl inside the barrel of the gun that causes the bullet to twist and fly straight and true. When it comes to firearms, Twist Rate is the rate at which the rifling is twisted. This twist affects how quickly the bullet is spinning when it comes out of the muzzle. This spin increases distance as well as accuracy. Think of a football being thrown, twist rate would determine how much that football is spinning. 
     Twist rate is denoted by the markings on the barrel, always as a 1:, as in one full rotation or twist, followed by another number which is the important part. This part is the space in which the twist takes place and it is measured in inches. So. 1:7 means that the rifling will make one full rotation or twist one time every 7 inches, a pretty fast twist rate. 1:12 will be a slower twist rate, with the rifling to make one full rotation once every foot. 
     So what though? Why should I care how much that bullet is twisting? As long as it’s got some spin to keep it going straight, what does it matter? Well, you’re kind of right, especially since these barrels are made by manufacturers that know what they are doing, they may have taken all of the guesswork out of this already. The very first AR-15 had a twist rate of 1:14 and was considered to be just fine at the time. These days 1:12 is about the slowest rate you’ll find for an AR-15. This is because faster is better in many ways. When it comes to spin there is an ideal, but if you should err, it should be on the side of too fast. A bullet spinning too slowly won’t stabilize enough to achieve its optimum velocity or best speed, so it won’t travel straightly, which will affect accuracy. Barrels with slower twist rates aren’t that common these days anyway, and when you do see them there is a good chance that it is on a longer barrel. This makes sense because the longer barrel gives more time to the bullet to get it spinning. Generally the shorter the barrel, the faster the twist rate. If your bullet weight weighs less than 55 grains, you might want to have a slower twist rate, even 1:8 or 1:9 would be better than 1:7. 55 grain bullets are pretty common and in 223 and 5.56 calibers 90 grain bullets are not uncommon. With these bullets a 1:7 Twist Rate would be recommended for 55 grain and higher. 
     A bullet spinning too fast could also affect accuracy, causing it to go off target. There are also reports of the rifling cutting into the bullet if it is spinning too fast, leading to fragmentation in flight. It is also possible that the centrifugal force could cause fragmentation, leading to a bullet going off target and losing part of itself on the way. You will likely find a faster twist rate on shorter barrels, since there is less time to get the bullet spinning. 
     It can be eye opening to look at the U.S. Military and its take on it. Military grade may not always be the best, but it pretty much always works and has a lot of practical research and experience behind it. The military uses a 1:7 twist rate, with bullet weights at or between 55 and 77 grains. Conversely, professional marksmen tend to use much slower twist rates even as slow as 1:18. Two different takes on twist rate by people who know what they are doing. 
     As a general rule, slower twist rates are for lighter bullets. Think of it as a lighter bullet needing less encouragement to get the spin going. A heavier bullet, on the other hand, will be harder to get spinning, which is why faster twist rates are recommended for them. 
     If bullet weights range from 40 grain to 90 grain then on a carbine you will want 1:9 for the lighter rounds 40 - 69 grain 1:8 for mid-range weights 62 - 77 and 1:7 for heavier 69 - 100+ 

Here are Twist Rates with how they are generally used on the AR-15 platform:
1:14 Twist Rate: Not commonly found on AR-15’s these days. These are best for longer barrels and bullets that are lighter than 55 grain. 
1:12 Twist Rate: Excels at varmint ammunition, and is great with mid 55-grain bullets and lighter. This twist rate works best on a varmint specific rifle using lighter loads. 
1:10 Twist Rate: This is great for lighter bullets and can handle your average 55 grain up to 69 grain. 
1:9 Twist Rate: Good for low to upper mid-weight, generally between 45 - 69 grain. 
1:8 Twist Rate: Works great with 16-inch barrels for a wide range of calibers. It’s a great all-around rate that will do well with most ammunition you are likely to use. 62 - 77 grain. 
1:7 Twist Rate: The fastest and most common twist rate due in part to the U.S. Military making this the standard for all of their rifles. It does well with the heavier grain bullets that they tend to favor. 69 - 100+ grain.