Leaking a little urine during pregnancy is a form of stress incontinence. Before you ask no, that has nothing to do with your state of mind! Stress incontinence refers to the additional stress that your bladder is under, because your growing baby is pushing on it, and is forcing your internal organs to move into a position they are not normally in. Additionally, your bladder can't hold as much urine as it can when you are not pregnant, again because your baby is in the way. Weak bladder control can also be caused by a urinary tract infection (UTI). If you suspect you have an UTI, it is important to call your doctor, because UTI's in pregnancy can lead to pre-term labor in some cases.
So, when does this happen? Most women start noticing that they have less control over their bladder sometimes during the third trimester of pregnancy. You can counteract a weaker bladder by going to the bathroom more often, staying hydrated well, and using panty liners in case you do lose a little now and then. You will regain complete bladder control soon after birth, when your muscles go back to normal.