"for just as Jonah was three days and three nights in the belly of the sea monster, so will the Son of Man be three days and three nights in the heart of the earth."  
Matt 12:40

Jesus was saying that the people would be given a sign to confirm His claims and it would be "the sign of Jonah". He would be in the grave three days and three nights after which He would come out (like Jonah), or rise from the dead. 

Note that the crucifixion did not take place on Friday as is commonly assumed. That error has been continued because of confusion over the statement that they should be taken down from the cross because the “next day was the Sabbath” (John 19:31). The Sabbath that was spoken of here was Passover, a "high Sabbath", a day before the weekly Sabbath, which accounts for three days and three nights in the grave.