Portia wounds herself because she wants to show that she can tolerate pain and handle difficulties. This is because she wishes to convince her husband, Brutus, that she is worthy of being privy to the secret burdens he must carry. Women are cast in this time period as being weak and unable to deal with the same sorts of pressures that men handle on a daily basis; by stabbing herself in the thigh, she attempts to make Brutus believe that she's "tough enough" to be part of the the secrecy.
It should be noted that even though she did this and Brutus agrees to tell her what's going on, she also succumbs to the pressure (just as the men around her who were involved end up doing!) by swallowing burning coals. Sometimes, ignorance is bliss!
She says she has but a man's mind but a woman's might. She wants to prove to her loving husband that she has the patience to bear the pain she has inflicted upon her self, and to hear the dark secrets he has within himself. Later as you will find in Act 2, Scene 4, Brutus tells his wife.