How does Portia prove her strength to Brutus?

Here's Portia, answering your question:

I grant I am a woman, but withal
A woman that Lord Brutus took to wife.
I grant I am a woman, but withal
A woman well reputed, Cato's daughter.
Think you I am no stronger than my sex,
Being so father'd and so husbanded?
Tell me your counsels, I will not disclose em.
I have made strong proof of my constancy,
Giving myself a voluntary wound
Here in the thigh. Can I bear that with patience
And not my husband's secrets?

Portia argues with Brutus, saying that she is a woman of a good reputation, with a famous, noble father, and a famous, noble husband. She, she says, is easily noble enough to be able to be trusted with Brutus' secrets.

Moreover, she has given herself a "voluntary wound" in the thigh - she has wounded herself, and, she says, if she can bear the wound with patience, surely she can bear her husband's secrets. Very odd, but - to the Romans - it would have been a real sign of her constancy and trustiworthiness.