Well you either follow (obey) rules, bend them or break them. If you break rules, you're obviously doing the exact opposite to what the rule says. Bending rules is somewhere in between... you're not exactly following the rule, but you're not breaking it either. Let's say you're following most of the rule, and re-interpreting the rest.

It can also be used relating to favoritism. Example. Our manager always bends the rules for David. When we are late to work, we get a warning from the manager. But, whenever David is is late he acts as if nothing happened.

It means not to follow the rules for a special occasion when it's necessary. Ex. "I don't usually go to the beach without wearing sun protection, but I'm willing to bend the rules this time since the temperature is very low." It also means to allow someone to do something that it's not usually allowed. Ex. "I never let anybody use my computer, but I'll bend the rules this time because I trust you so much."