Rubato is Italian for stolen or robbed and refers to timing the notes, specifically not hitting the beats in strict time. Rubato is playing around the beat: sometimes coming a little before it, or a bit late, or slightly speeding up or slowing down a few beats. The purpose is to make the music more expressive.
Most often rubato is used in lyrical sections of the melody by the singer, while strict time is maintained by the instrumental, accompaniment, musicians. When done tastefully rubato adds a nice touch. When overdone there is a danger of the melody losing all sense of the beat. Some singers use it more effectively than others.