Basically, that means 'shut up'. You usually say it while holding a hand up to stop the person from talking. It implies that your ears aren't listening to that person (because you find him/her annoying), so he/she could as well talk to your hand.

This sentence is used when someone won't stop talking or arguing. It is also accompanied by the gesture of raising your hand like a stop signal. Do not use it in formal situations as it would be considered very ill mannered. It is effective with young children when they keep asking for something that they can't have.

It's an informal, sarcastic, English slang phrase, the full version is 'talk to the hand because the ear's not listening.' A person who uses this phrase means 'I am not interested in talking to you.' Hope that helps!

Meaning (With outstretched vertical palm) Shut up - I've no interest in hearing what you've got to say.

The gesture can be even more sarcastic when someone shows his hand "speaking" as if there's a puppet on it. Once one of my friends, being in a temper, drew eyes and a mouth on his palm. It wasn't funny that time.