i-adjective
Describes physical thickness of objects, body parts, or lines. For people, 太い can mean 'fat' but is less polite than 太っている.
この木の幹はとても太い。
The trunk of this tree is very thick.
彼は足が太い。
He has thick legs.
i-adjective
Describes a person who is thick-skinned, bold, or unashamed in a negative way. Often used in phrases like 太い奴 or 太い神経.
あんな嘘をつくなんて、太い奴だ。
He's a brazen guy to tell a lie like that.
彼女は太い神経の持ち主だ。
She has a lot of nerve.