The phrase means that something is not over until the veryend - there may still be time for circumstances to change. It comes from, I think, the Ring Cycle, the extremely long opera by Wagner which ends with the diva dressed as a Valkyrie singing a final song. For some reason, a lot of opera divas tended to be rather well-built ladies, hence the expression.
Andy is certainly right, but - for a little more information on the phrase's origin etc - click here. That will link you to a web-page which might help.
Supposedly it is supposed to be
'Its not over til the fat lady sinks'
because in snooker or billiards or something the game is over when the black gets potted and the black is called the fat lady.
Andy Hughes is right but mainly used as a baseball term that the national anthem should be sung before you leave the stadium. And female singers with big voices big girls themselves