Prop 13 puts a cap on how high the city could increase the assessed value of property. As such, cities could not afford to build more schools, parks, fire stations, police stations, infrastructure, etc to accommodate the influx of residents moving into the newly built houses.
At least not at first.
Over time, all income from the property taxes coming in could, in theory, pay for it, but that would require new residences to live in a community with no local parks, schools, etc for years before the taxes could be acquired, saved up, and then used to build the additional infrastructure
So the cities were pushing for the home developers to pay for the additional infrastructure.
However, the developers building the houses couldn't feasibly lower their profits any further. They ended up raising prices of the newly built homes to compensate for the added expense. However, this made the houses to expensive to sell. No one could afford the houses.
So in 1982, Senator Henry Mello, and Assemblyman Mike Roos legislated a way around Prop 13 so that new communities could finance the upfront costs of the needed public services with a loan.
Mello-Roos legally circumvents Prop 13 because it is not levied on the assessed value of the property. It is a flat payment to pay off the loan. The schools and parks can get a one time extension if the new influx of property taxes wouldn't adequately replace the income from the mello-roos. Never the less, mello-roos do normally get paid off over time.
Homeowners even have the option to pay off their property's share of the loan early, and live out the rest of their days in a mello-roos free property. They can even sell the property to the next owner mello-roos free.