Remember why you started looking
Most people start looking for reasons that have nothing to do with pay: progression, management, the work itself. A counter-offer changes the number and nothing else.
What happens next
Your employer now knows you were ready to leave. That changes the relationship, and many people who accept find themselves looking again within a year.
When it can make sense
If the counter-offer comes with a real change in role or reporting line, in writing, it is worth considering properly.