Literally 'stomach full' — being full from eating; equivalent to 'I'm full'.
ランチを食べ過ぎて、今はお腹いっぱいだ。
I ate too much lunch, and now I'm full.
子どもたちはお腹いっぱいになって眠ってしまった。
The children fell asleep full.
『もうひと皿？』『いいえ、お腹いっぱいです。』
'Another plate?' 'No, I'm full.'
Used adverbially to mean 'to one's heart's content' or 'as much as one wants' (e.g., eat to one's heart's content).
食べ放題でお腹いっぱい食べたから、当分外食はいいや。
I ate my fill at the all-you-can-eat, so I don't feel like eating out for a while.
休日は趣味に没頭して、お腹いっぱい楽しんだ。
On my day off I immersed myself in my hobby and enjoyed it to the fullest.