noun
both people; two people
Honorific noun used to refer to two people respectfully. Often used in formal contexts or when speaking about others politely.
お二方ともお元気そうで何よりです。
I'm glad to see both of you looking well.
こちらのお二方が今回の受賞者です。
These two people are this year's award recipients.
noun
two directions; both directions
Refers to two directions or both sides. Can be used literally for physical directions or figuratively for approaches or aspects.
交差点では二方から車が来るので注意が必要だ。
At the intersection, cars come from two directions, so you need to be careful.
この問題は二方から検討する必要がある。
This problem needs to be examined from both directions.
両方 means 'both' in a general sense (both things, both sides), while 二方 specifically refers to two people (honorific) or two directions.
二人 is the standard word for 'two people', while 二方 is its honorific counterpart used in polite contexts.
Compound of 二 (two) and 方 (direction/person). The honorific sense derives from the respectful use of 方 to refer to people.