A polite way to refer to a person (that gentleman / that lady / he / she), used to show respect.
あの方は私の大学の教授です。
That person is my university professor.
あの方はどなたですか。初めてお目にかかります。
Who is that person? This is my first time meeting them.
彼の方ではなく、あの方にお話を伺ったほうがいいでしょう。
Rather than him, it would be better to ask that person.