As Izhaki's answer arduously points out, if you really want to know the answer to a question about your users, you can ask them, or ask a test group reasonably similar to them.
Good Design Meets Expectations
'Relevance' probably came from the technical reference to the algorithm that drives the search i.e. results are quantifiable and decreasingly relevant the specific to the query in question, in ways determined by the design of the algorithm.
The point is that now it has become a standard way of referring to this default sort, and that changing it for the sake of clarity may simply result in a point of confusion, or simply a visual snag in the UI. Stick with the standard.
If it's default, it might not be worth worrying too much about.
In a UI where, within any single search session, a user will always see results sorted (by default) by 'Relevance' unless they change to something else, it matters much less what the label is. Provided the UI also contains supportive copy e.g. 'Sort by:', then they don't even need to be able to interpret it, they only need to be able to recall what it is if they decide to change back e.g. from 'Price' back to 'Relevance'.
If, however, this is a UI where the user can do something as complex as build and save filter views, where all the component labels need to be understood clearly, then I think, and this is where my answer ventures into opinion, you may have a point in doubting the use of 'Relevance' especially when compared to to something like the recognizably more approachable and palatable 'Best Match'. You'd be trading in a $10 word for a couple of $1 ones.
To circle back around the testing point, this is the type of thing you could test with users, but it's testing that will involved a lot of thinking and work, and you'd need to be sure it's what you should prioritizing your time on.