When you acclimate yourself to a situation, you become used to it. It usually means getting accustomed to a particular new climate, but it can also mean getting used to other situations, such as a new school.
The word climate in the word acclimate should give you a clue as to the word's meaning: to get used to a specific climate. Nature allows the human body to acclimate itself to various weather conditions. For example, people moving to higher altitudes will develop more red blood cells in order to absorb oxygen better. This is their bodies' way of acclimating to the thinner air. It takes a while for the body to become acclimated to a new climate.