Asceticism is rigorous self-denial, particularly the rejection of the pleasures of the world. If you don't drink, smoke, eat sugar, see movies, use the internet, or have a cell phone, then you are already practicing a kind of asceticism.
Asceticism comes from the word ascetic, which comes from Greek roots meaning monk, and practice or exercise. Historically, Asceticism was a rigorous, laborious lifestyle, involving the denial of pleasure and rest as a way of expressing spiritual devotion. Now we use asceticism as a synonym for austerity.