The purpose of the Stable Homes Act is to create a grant program that helps local governments set up or improve eviction diversion programs. These programs aim to prevent evictions by providing support and resources to tenants and landlords before formal eviction proceedings begin. Key provisions of the Act include the establishment of a pilot program by the Secretary of Housing and Urban Development within one year of the law's enactment. Local governments can apply for grants to fund their eviction diversion initiatives.