An instruction to indicate that a player can freely express the music by changing the tempo. The player can slow down or speed up as they wish. This was very common in music from the Romantic period.
Composers like Liszt and Chopin were highly skilled in using rubato to effectively convey the emotion in the music.
For example, Chopin's Mazurka No. 1 - it's a great example of how composers play with the music:
Another example is Prelude from Debussy's Suite bergamasque - try and count the four beats in the bar and you'll hear that the music does not follow a strict metronome time. It speeds up and slows down, which is much more expressive than a set number of beats per bar.