Using this dictionary explanation, algebra is:
“ A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.”
Now that was the easiest explanation out of several that I read.
Basically we are going to use letters to help us solve problems where we are not really sure of the actual numerical value. Here is an example of what we are trying to aim for as a worked example, look here now