The journey to mecca that each muslim is expected to take at least once is known as
the holy pilgrimage.
the haj.
the sacred duty.
the qur'an.

The journey to Mecca that is expected to be done by muslims at least once is called: Hajj

Mecca is considered to be the Holiest city of muslim (the only city that can be considered as holiest city beside Mecca is Medina). Adult muslims are expected to conduct Hajj at least once especially if they are physically and financially capable, and their family could take care of themselves during the period of their journey.