Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.
The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")
Using math operations one can relate x values with y values via an equation of the type:
y = 2 x - 5
where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.
For example, try the number x = 0
and see which y number connects with it:
y = 2 (0) - 5 = 0 - 5 = -5
Then you say that the number 0 in the Domain connects with the number -5 in the Range.
This relationship can also be given with coordinate pairs of the form:
(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.
The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.
I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.