1Right; the right-hand side or direction.
駅はこの通りの右にあります。
The station is on the right side of this street.
車は右側通行の国と左側通行の国がある。
There are countries where traffic drives on the right and others where it drives on the left.
右を見て渡りなさい。
Look to the right before crossing.
2The right hand (of the body).
右手で箸を持って食べます。
I eat holding chopsticks with my right hand.
彼は右が利き手だ。
He is right-handed.
彼女は右に軽いけがをしている。
She has a minor injury on her right side/hand.
3In formal/legal vertical-writing documents, '右' refers back to what was stated above/previously (since vertical columns read right to left) — a formal, document-style usage, as in 「右の通り」 ('as stated above').
この書類は縦書きなので、右が先に来る。
This document is in vertical format, so the right (i.e., the above-mentioned part) comes first.
契約書には「右の条件に同意する」と記されていた。
The contract stated, 'I agree to the above-mentioned conditions.'
4The political 'right' or right wing; conservative or right-leaning positions/groups.
その党は右の立場を取っている。
That party takes a right-wing position.
右派のグループがデモを行った。
A right-wing group held a demonstration.
政治の右・左の対立が強まっている。
The political divide between right and left is intensifying.
5An old, formal usage meaning 'the superior one' when comparing two things. It originates from traditional contests (e.g., sumo, poetry competitions) where competitors were split into a 'left' and 'right' side, and the winning side was referred to as such. This sense is essentially unused in everyday modern Japanese.