A complex and controversial notion which has been used both to distinguish the moral from the non-moral and to distinguish the moral from the immoral - two jobs which tend to get in each other's way.
'What if everyone did that?' is often a relevant question in moral contexts; but 'did what exactly?'. The same action can be described in many ways. And what counts as 'everyone'?
Presumably everyone with certain characteristics or in a certain situation, but which characteristics or situations? As for distinguishing the moral from the non-moral, no doubt if I act in arbitrary ways I cannot claim to be acting on a moral principle - but will I be acting on any other kind of principle either? And what counts as 'arbitrary'?
These questions of course give only the general flavor of discussions in this area; and though the terms are often confused, one should distinguish the universal (as against particular or individual) from the general (as against specific): 'Always help the blind' is universal but specific.
The appeal to universalizability in ethics dates from Immanuel Kant (1724-1804).
D Locke, 'The Trivializability of Universalizability', Philosophical Review (1968)