When quarians of the Migrant Fleet reach young adulthood, they must leave their birth ship and find a new crew to accept them as permanent residents. To prove themselves, they must recover something of value. This is offered to their prospective captain as proof that they will not be a mere burden on the shoestring resources of the ship.
This process is called the Pilgrimage. Stripped of ritual, the Pilgrimage is merely an attempt to maintain genetic diversity within the small, relatively isolated population bases that make up the Migrant Fleet. If the young stayed and married within their birth vessel, the risk of inbreeding would increase sharply.
Quarians are surgically fitted with their various immunity-boosted implants in preparation for leaving on Pilgrimage. Having grown within the sterile, controlled environments of the Migrant Fleet ships, quarians have virtually no natural immune system.