First, let’s talk about funds. When a GP (e.g. a venture capital firm or private equity firm) has a certain investment mandate they need to satisfy, they will launch a fund and, in effect, pool capital to fulfill that directive.
Similar to how companies offer diverse products, firms will create distinct funds with different strategies to reach various markets or geographies. And often, if a fund is successful, the financial sponsor will launch another one that shares similar characteristics to the one that preceded it.
A series of funds that share the same strategy, geography and financial sponsor is what we call a fund family. Typically funds in a family will follow a similar naming convention (e.g. Fund II, Fund III and Fund IV), although there are some exceptions.