I heard this phrase today when I nipped out to the shop to grab some lunch. There was a dad doing food shopping with his tree daughters and he said that he needed to buy some cereals. The girls weren’t too enthusiastic about it for some reason, but he said ‘I’m nearly through my (let’s say tangerine granola), and I do like my tangerine granola, you know!’
This is quite a common phrasal verb and it can mean:
1) having finished an activity or piece of work
– I’m not sure what time he’ll be through with his meeting.
– Only one more letter to write. I’m nearly through.
2) to have ended a relationship
– I’ve told Larry I’m through with him, but he keeps bothering me.
3) to have finished using something
– Let me know when you’re through with the hairdryer.
4) to have decided to stop doing something that you used to do
– Are you through with politics?
(All examples: MacMillan Dictionary)