A static residential proxy is an IP address that an internet provider registered as residential, served from datacenter hardware so it is online around the clock. You rent the address itself, per IP and per period, and it stays yours for that period. Websites see a home-registered address; you see one that never changes underneath you.
The product has two names on the market. Static residential says what a website sees: an address on a consumer internet provider's network. Static ISP says where it comes from: a provider's address block, hosted in a datacenter. Here they are one product.
It is the non-rotating counterpart of the residential pools: pick it when a target has to see the same address for weeks, not for a session.