When you're telling a story about something that happened, sometimes you don't want to tell everything that a person did. You just want to tell what happened last. To express this, you say that someone "ended up ___ing". For example:
We had a great time sitting around talking, and we ended up going to bed at about four in the morning.
Jason looked for a job for about 6 months, and he finally ended up taking a job waiting tables at a sushi restaurant downtown.