1"Originally", "from the start", or "by nature" — describes how something was true from the very beginning or is an inherent trait. Very common in everyday conversation. Usually written in kana.
もともと彼は医者になりたかった。
He originally wanted to become a doctor.
この建物はもともと学校だったが、今はオフィスになっている。
This building was originally a school, but now it's an office.
その計画は、もともと無理があった。
That plan was unreasonable from the start.
もともと彼女は人見知りなタイプだ。
She's the shy type by nature.
2Mainly used in the pattern "〜てもともと" / "〜でもともと" to mean "even if it doesn't work out, you're no worse off than before" — an idiomatic way of saying there's nothing to lose by trying.
ダメでもともとだから、とりあえず申し込んでみよう。
There's nothing to lose, so let's just apply and see.
断られてもともとだと思って、思い切って頼んでみた。
Figuring I had nothing to lose even if I got turned down, I went ahead and asked.