What word or phrase does your mother always say?
Testing a pre-release (potentially unreliable) version of a piece of software by making it available to selected users. This term derives from early 1960s terminology for product cycle checkpoints, first used at IBM but later standard throughout the industry.
"Alpha test" was the unit, module, or component test phase; "Beta Test" was initial system test. These themselves came from earlier A- and B-tests for hardware. The A-test was a feasibility and manufacturability evaluation done before any commitment to design and development. The B-test was a demonstration that the engineering model functioned as specified. The C-test (corresponding to today's beta) was the B-test performed on early samples of the production design.
An item "in beta test" is thus mostly working but still under test. In the Real World, systems (hardware or software) often go through two stages of release testing: Alpha (in-house) and Beta (out-house?). Beta releases are generally made available to a small number of lucky (or unlucky), trusted customers.