There's no single commonly-accepted definition; the dividing line has shifted over time.
In 1977 when the Apple II, PET and TRS-80 collectively invented home computing the difference was pretty obvious: the computers had the ability to display good-quality text, and provided a textual interface.
That codified into a home computer having a keyboard and starting up in some sort of operating enviroment into which software was loaded on top — computers mostly had decent quantities of RAM, whereas a console would have a negligible amount and would usually boot directly into a ROM dedicated to one piece of software, without anything much of an OS.
The idiomatic home-use machines also tended to provide a programming language as a shell for a while, but that ceased entirely with the 16-bit machines and was only a rule-of-thumb in the first place.
Another axis of distinction is peripherals and expansions: use cases for computers tended to vary enough that a diverse range of peripherals would appear, such as disk drives, printers and light pens. So computers had much greater internal hardware diversity. The Apple II is the archetype of that with expansion slots right in the case.
Nowadays consoles still tend to be more single-task focussed but that expresses itself only in appropriate specialisation of the OS; the distinction is more a question of positioning and business model. A console is built primarily for games and sold at a loss on the presumption that the user will buy enough different pieces of software to make up the difference whereas with a computer, if it comes with an office bundle and a web browser then it is expected that a user may never buy another piece of software again.