Expressions are 'variable watches' through which you can type any perl expression to be evaluated. The more interesting expressions use variables that depend upon the current state of the regex. $1-$9, $`, $&, $', and pos() are all available for use.
Breakpoints allow you to write a conditional based on the above expressions. When the breakpoint expression returns non-zero, any playing of the regex (forwards or backwards) will cause it to stop and wait for further input.