Around and About

In British English, around is used to talk about position or movement in a circle or a curve.

Why are you walking around the house?
They all sat around the table.
Men were standing around the street corners.
They live somewhere around here.

In British English, around is also used to talk about going to all parts of a place or giving things to everybody in a group.

Could you pass the salt around, please?
We walked around the village. (= We went to almost all parts of the village.)

Indefinite movement and position

Both around and about can be used to talk about indefinite movements or position.

Children usually rush about. OR Children usually rush around.
Why are you standing around/about without doing anything?
‘Where is John?’ ‘He was somewhere around here.’

Both around and about can mean approximately.

It is about ten o’clock. OR It is around ten o’clock.
Around fifty people attended the meeting. OR About fifty people attended the meeting.

American English

In American English, about is mostly used to mean ‘approximately’. For other meanings Americans use around.