A mitre is any cut in wood that is not 90 degrees. They can be made with a mitre saw, hand saw with mitre box, table saw with mitre gauge or a band saw. Mitre joints -- where two cuts are joined -- are common in picture frames and fine furniture.
To get good mitres, you need to understand what makes the mitre joint work. The cumulative degree of two or more mitres must be 90 degrees. There are preset stops on most mitre saws at 22.5 and 45 degrees. If one mitre is sharp and measures 50 degrees, then the other mitre must be cut at 40 degrees. Adjust the saw blade accordingly when mitres are at uncommon angles.
It can be difficult to measure mitre degree. The best way is to cut test mitres with a piece of straight wood. Cut a mitre at approximately the degree that you think you need. Cut another piece at the same degree. Test the pieces together on your workpiece. If there is a gap on the back of the joint, the angle is too shallow. If the gap is on the front of the mitre, it is too steep. Adjust the saw blade angle, cut both pieces and try again until the gap closes tight.
Bad mitres are often the result of blowout caused from lack of support of the wood. The saw blade cuts through the wood and, when exiting the wood, blows chips or splinters out the back of the mitre. To get clean mitre cuts, place another piece of wood behind the wood being mitred. You will cut through both pieces of wood, but the wood in the back prevents chips and blowout.
For really clean mitre cuts, use a table saw. They often have larger blades than mitre saws, and are more solid. All table saws have mitre gauges and gauge slots. When cutting mitres on small mouldings, table saws have superior visibility. The operator simply makes the mark on the moulding, slides it up to the blade while the saw is off, positions the blade to the mark, turns the saw on and makes the cut. It's easier to control small pieces on a table saw, and they cut cleaner.