It means to reach the limit. The word "max" is short for "maximum" (the greatest amount possible), so to max out means to reach the maximum. If you say "I was maxed out" it could mean you were exhausted and couldn't do anything more that day (depending on the context). For example: After waking up early and driving 10 hours, I was maxed out and went straight to bed.

Explained perfectly above

In addition to the other excellent answers, in some contexts it can have a more positive meaning, something like "making the most of the opportunities. You might hear a group of friends say that the "maxed out the weekend", meaning that their weekend was full of great activities and they couldn't have fitted in any more fun than they did. But more often, and certainly in your example "I was maxed out", it means that I have spent more money or more energy than I had, and I'm now broke or exhausted.

To go over the limit. My credit card is maxed out! meaning that it doesn't have any more credit available.