Why is my Minecraft: Xbox 360 Edition game lagging so bad?

I loaded up and started a new survival world about a month ago, and just yesterday, my game started to lag very badly. I have to hold down my trigger for a very long time to eat, and when I sleep, it takes a long time sitting in the bed to start the next day. Also, item pick ups are very delayed (when I'm mining, the blocks I destroy don't go to my inventory until about 3 seconds later), and when I kill mobs, they lag out and float in the air for a few seconds after being killed.

There might be something wrong in your local internet connection. Try asking your neighbor for how the internet is doing. If they will be telling you it's bad That is a possibility.

Not up to date

Well if you have played on the same world for a month and it was like constant hour after hour every day then there's a possibility that if you built too much stuff or if you have built alot of things in the first place. Or the possibility that your xbox360 can't keep up with some games?