Why do I need to know tu parles?
You should know tu parles because you might hear it in response to something you've said.
What does it mean?
Literally tu parles means ‘you’re speaking’, but when used an interjection, tu parles ! is a way of expressing incredulity or disbelief.
The best English translation is perhaps expression ‘no way’, but it can also mean ‘you must be kidding’, 'you're having a laugh', 'yeah right’ and ‘what a load of rubbish’. French people will often use it when they don’t agree with you, or are sceptical abut something you said or perhaps when they are acknowledging your joke or an ironic remark.
Here are some examples:
Les hommes politiques sont tous honnêtes – Politicians are all honest people
Tu parles ! – Yeh right, you're having a laugh!
Ta belle-mère me semble une personne très gentille – Your mother-in-law seems like a really nice person
Tu parles ! Elle me déteste depuis le début – Yeah right! She hated me right from the beginning.
Si on part maintenant je pense qu’on arrivera en temps – If we leave now I’m sure we will get there on time.
Tu parles! Tu as oublié qu’il y a la grève? – No way! Have you forgotten that there’s a [transport] strike going on?
There is no vous-version of tu parles, so the expression is too colloquial to be used in front of your boss or in formal settings.
You could use vous rigolez or laissez moi rire if you want a formal response to someone you don't agree with.
Other expressions similar to tu parles that don't include a first person pronoun is the more formal mon oeil ('my eye') or the (very) colloquial mon cul ('my ass').
Another option is foutaise, which can be translated to 'crap' or 'bullshit'. But, as you see from the translation, you should be a little cautious when using it.