〜てしまう

end up doing / completely

Says that an action is completely finished, or that something happened that you regret or did not mean to do.

Readings

Conjugation rules

Put the verb in the て-form and add しまう: 忘(わす)れる becomes 忘(わす)れてしまう.
しまう conjugates like a godan verb: 忘(わす)れてしまいました, 忘(わす)れてしまった.
In conversation てしまう often becomes ちゃう, and でしまう becomes じゃう: 忘(わす)れちゃう, 読(よ)んじゃう. The past is ちゃった and じゃった.

ichidan

忘(わす)れる(to forget)忘(わす)れてしまう

godan

読(よ)む(to read)読(よ)んでしまう

行(い)く(to go)行(い)ってしまう

宿題(しゅくだい)を忘(わす)れてしまいました。

Oh no, I forgot my homework.

本(ほん)を全部(ぜんぶ)読(よ)んでしまった。

I read the whole book.

Context tells you which meaning is meant. With a mistake or an accident it expresses regret; with words like 全部(ぜんぶ) (all) it is usually about finishing.
It can also mean you did something without meaning to: 笑(わら)ってしまった (I couldn't help laughing).

Assuming it is always negative. 全部(ぜんぶ)食(た)べてしまった can simply mean you finished it all.