Full Idea
We think of things existing when they are in time (though possibly at all times), but universals do not exist in this sense, so we shall say that they 'subsist' or 'have being'.
Gist of Idea
Normal existence is in time, so we must say that universals 'subsist'
Source
Bertrand Russell (Problems of Philosophy [1912], Ch. 9)
Book Reference
Russell,Bertrand: 'The Problems of Philosophy' [OUP 1995], p.57
A Reaction
Russell picked up the word 'subsist' from medieval philosophy. This idea brings the full Platonic metaphysics with it, which is tricky, to say the least. But what can you do? Admitting the content of thought brings baggage with it.