What does bijection mean with regards to Combinatorics and Sets? I think I understand the 2 conditions that are necessary for a function to be bijective, but in a book of Combinatorics I am reading it talks about Bijections with sets and with combinatorial problems, and doesn't explain what it is very well in my opinion. It simply says it's a one-to-one correspondence between different items... What does a bijection mean then with regards to Combinatorics and sets?
For example, earlier in the book it gave this problem:

Suppose that $a,~b,~c,~d$ and $e$ are positive integers. How many solutions are there to the equation $$a+b+c+d+e=11$$?

This can be found by considering $11$ items and $4$ gaps between different items out of the $10$ possible gaps, so the solution is $\binom{10}{4}$. I understand this perfectly.
Later, when talking briefly about bijections it says of the aforementioned problem that the coding (of $4$ objects that can be chosen of one and $6$ of the same type of object that can't be chosen (in this case, gaps)) is 'unique and reversible, or, in other words, that it represented a bijection.'
What does it mean by this? What bijection is it talking about? I have no idea. Also, I don't understand what it means by reversible.
Thank you for your help in this very basic question.

It is like speed-dating.
If $10$ women want to date $10$ men simultaneously, you have to match every woman with a man, every man with a woman, such that every man has a woman to date and every woman has a man to date.
To each element of the first set (the women) is associated one and only one element of the second set (the men), and reciprocally.
