There are three reasons why we wash our hands every morning upon waking up from our sleep.
1. When one sleeps, their neshama leaves their body and in its place a ruach hatumah finds room to rest, with the intention of causing them to sin. When one wakes up and their neshama returns to their body, the ruach hatumah is forced to leave and does so through their fingers, leaving a trace of ruach hatumah on the fingers. The ruach hatumah then remains there until one washes their hands three times the proper way. (The Chai Adam adds that if someone has no יראת שמים then this ruach hatumah can come onto them even when they are awake!)
2.When one wakes up in the morning, he/she is a new creation, ready to begin a fresh day of Avodas Hashem, and is like the Kohain in the Bais Hamikdash who washed his hands at the beginning of each day’s avodah.
3. One’s hands must be clean for davening, and since during our sleep we usually touch unclean parts of our body, there is a mitzvah to wash our hands before davening.