Definition:
Size is added to paper during manufacturing to make it more or less absorbent. The less size there is in a sheet of paper, the more it will absorb the paint.
Size is also the term used for a glue (sometimes made from rabbit skin) put on a canvas before priming to protect it from the oil in oil paint. It's also used to seal wood panels before painting and on plaster, if you don't want the paint to seep into the plaster.
Lastly, size can also mean the physical dimensions of a sheet of paper (see for example A Paper Sizes), or a canvas. The context in which the word is used will tell you what is meant.
