To look after is to watch over and protect a person, animal, or thing. Look after the children, look after yourself, who will look after the dog.
It is the everyday phrase where care for is formal and mind is regional. Look after yourself works as a goodbye in British English. Note that look after somebody and look for somebody mean entirely different things, which learners meet early.
1phraselook afterTo watch over and protect a person, animal, or thing.
“Could you look after our cat while we're away?”
look after is a caring for.
Also accepted in games: care for, take care of
Practised in Everyday Verbs, Phrasal Verbs