What does it mean to test God? I remember that while Jesus was being tempted in the desert by the devil, the devil had asked Him to jump down from a height, because the angels would be sure to rescue Him. But Jesus answered that one should not test God.

What does it mean to "test" God?
In this context, it meant to demand that God prove Himself.  

My answer to this question address this, as does the one on the link @Caleb provided in the note above.

The short version of it is that throughout Biblical history, from the Exodus on, God has shown little patience with people demanding He prove that He exist, particularly the Israelites, who had seen His miracles time and time again.

In this context, the conversation could be paraphrased as this, (and this is a rough paraphrase, reading in my understanding of the context):

Satan is tempting Jesus to prove who God is, and who He is.  Satan already knew who He is, so the essence of Satan's asking Jesus to do this is "Oh, yeah, if you're God's son, and God is so powerful, then prove it."  Christ, recognizing Satan's goading as a mockery of God, refused.  In doing so, He showed not only His obedience to God the Father, but also His perfection and inability to be goaded and tempted by Satan.

Satan's temptation was no different than the mocking given to Jesus in Matthew 27:37-42.