Early history of the savings and loan association
The savings and loan association became a strong force in the early 20th century through assisting people with home ownership, through mortgage lending, and further assisting their members with basic saving and investing outlets, typically through passbook savings accounts and term certificates of deposit.

The savings and loan in the early 20th century (in the U.S.)
The earliest of mortgages were not offered by banks, but by insurance companies, and they differed greatly from the mortgage or home loan that is familiar today. Most early mortgages were short term with some kind of balloon payment at the end of the term, or they were interest-only loans which did not pay anything toward the principal of the loan with each payment. As such, many people were either perpetually in debt in a continuous cycle of refinancing their home purchase, or they lost their home through foreclosure when they were unable to make the balloon payment at the end of the term of that loan.
This bothered government regulators who then established the Federal Home Loan Bank and associated Federal Home Loan Bank Board to assist other banks in providing funding to offer long term, amortized loans for home purchases. The idea was to get banks involved in lending, not insurance companies, and to provide realistic loans which people could repay and gain full ownership of their homes.
Savings and loan associations sprung up all across the United States because there was low-cost funding available through the Federal Home Loan Bank for the purposes of mortgage lending.

Further advantages

Cooperative banking
Savings and Loan crisis