The paste buffer is a holding bucket for all of the text you will copy, which you will then be able to access later to paste onto any pane.
It is actually a stack, so each item copied from Copy mode is added at the top of the stack, and every new item is added at the top with every other item moved down by one. Each item in the paste buffer is assigned a number based on the order in which it went into the stack.
Now that you've grabbed some text, you want to pull it from the paste buffer to get it back.
In any program that runs within tmux, move your cursor to the point where you want the text to be pasted and press <Prefix>, ].
For example, let's fire up nano:
$ nano
Once we do this, paste what we last copied with <Prefix>, ].
Sure enough, our text appears! Notice the nice symmetry, where you use <Prefix>, [ to enter Copy mode, and <Prefix>, ] to paste the text.
Now <Prefix>, ] is nice to paste the...