When asked to simplify something in mathematics, this generally means bringing it to the most basic, concise form while still meaning the same thing.
For example, consider the fraction "10/5". This could be simplified by writing is as "2". There is no way we could further make this more concise, so we now say it is simplified.
Another example, consider the fraction "10/15". We notice that we could divide both the numerator and denominator by 5, giving us "2/3". At this point the numerator and denominator share no other common factors so the fraction is simplified.
You can also simplify expressions. For example, consider "2x + 5x". We notice that both of these terms contain x, so we could simplify is simply as "7x".
Another example: "(6x * 2) / 3x" -- we notice that both that the x's cancel each other out, giving us "(6 * 2) / 3". This could then be further simplified as "12/3", which could then be finally simplified as "4".
So to recap, simplifying means bringing an expression so the simplest form possible, which still representing the same thing. The approach you take to simplifying an expression will vary from problem to problem, and may involve things such as reducing fractions and combining like terms.