Fittings are the way pipes are held together and there are thousands of fittings you can choose from, in varying sizes and materials. But all of them perform basic functions that will help you identify exactly which ones are needed.
There are two basic designations for pipe fittings - male and female. And these designations refer to the threading on the fitting. Male threading is on the outside and threads into the female threading - which is on the inside of the fitting.
NIPPLE fittings are designed to extend a line or provide a proper threading at the right location. COUPLINGS connect all standard sizes of pipe in a straight run. Regular couplings fits the same size pipe at both ends. While reducer couplings let you step down from one pipe size to another one. 
ELBOWS are designed to change the direction of the pipe. Most common are 90 and 45 degree elbows which have inside threads on both ends. TEES are used wherever two pipes intersect and are used to run three pipes in a "T" shape. It's also important to note that Tees are always referred to by the dimension of the main line first, then the branch line.
Another type of fitting is a union. Unions serve the same purpose as couplings, but they compensate for the fact that all pipes have right hand threads. Use of unions make it easier to take sections apart for repairs.