These are a few indicators of a buyers seriousness:
Cash buyer or preapproved
ready to close ASAP
limited or no contingencies
willing to pay close to the asking price
Hope this is helpful.
The "Eckler Team"
Michael Sanuders & Company
Also, while not mandatory, an offer of earnest money would be helpful. If they have an immediate "investment", such as earnest money, then you know that first of all, they actually have some cash and second, that they are willing to risk that cash. (The definition of "earnest" is fervent, purposeful, determined, resolute, serious, sincere. Earnest implies having a purpose and being steadily and soberly eager in pursuing it.)
Hope this helps.
Serious about buying - check Bill's answer.
Serious about buying YOUR house - check Jeff's answer.
Other than that, it does not matter if the buyers look at your house 100 times, they might be serious, but it does not make any difference in accomplish YOUR goal.
Hopefully they are working with a Realtor, and the Realtor can consult with them about the advantage of your house vs others to make this work!
In this market buyers are much more cautious and may take longer to make a quality offer. I would expect more contingencies than you might have expected 2 years ago. Good luck, but buyers controll the market now and sellers will have to work a little harder than a few years ago.