The pilgrimage every able Muslim who can afford it is expected to make once in a lifetime, performed in the month of Dhu al-Hijjah. Its rites coincide with Eid al-Adha. Distinct from Umrah — the 'lesser pilgrimage' — which can be performed any time of year and is far shorter.
In Dubai you'll notice the rhythm of it: colleagues away on Hajj, the greeting 'Hajj mabrook' on their return, and the title Hajji sometimes attached to those who have gone.