The most important Muslim practices are the Five Pillars of Islam.
The Five Pillars of Islam are the five obligations that every Muslim must satisfy in order to live a good and responsible life according to Islam.
The Five Pillars consist of:

Shahadah: sincerely reciting the Muslim profession of faith
Salat: performing ritual prayers in the proper way five times each day
Zakat: paying an alms (or charity) tax to benefit the poor and the needy
Sawm: fasting during the month of Ramadan
Hajj: pilgrimage to Mecca

Why are they important?
Carrying out these obligations provides the framework of a Muslim's life, and weaves their everyday activities and their beliefs into a single cloth of religious devotion.
No matter how sincerely a person may believe, Islam regards it as pointless to live life without putting that faith into action and practice.
Carrying out the Five Pillars demonstrates that the Muslim is putting their faith first, and not just trying to fit it in around their secular lives.