How to remove dark spots from wood kitchen countertop

Looks like oil or grease of some sort. When you have real wood counter tops like that (which I NEVER recommend for this very reason), it is HIGHLY imperative that they be thoroughly sealed and the sealing maintained so that cooking oils and food grease cannot get into the wood, especially at the plank ends, as it has here. The reason it is so imperative is that there is no way to remove it now. The best hope is to have the entire surface sanded down to the raw wood again, bleach it (wood bleach, not laundry bleach) then try to stain it all to match the shade of those stains.

Try using a flat putty knife and scrape it across the stain at about a 45 degree angle. Scrape “with the grain” and start softly. Increase the pressure if it’s working.

Make sure the putty knife is smooth.

You may need to touch up the stain when finished.