We offer our unit in a 120 or 277 volt version. A customer just told me he is using a "120/208" system. What does that mean and will our 120 volt rated product work with it?

208 is usually 3 phase. It's stepped down to 120 for the 120 common single phase products to work. Single phase 208 is usually available too It's just never stepped down to a 120 3 phase panel. No point.

277 comes from a 480 three phase system. 277 is usually reserved for lighting and has a separate panel. 277 is single phase too.

There is a chance, that your customer has a higher voltage such as 480, but doesn't know. There would be a panel dedicated to lighting at 277 V if he did. The 480 would typically be used to run the HVAC systems.

Yes, your product would work on single phase 120 on a 120/208 V system. The customer probably has 120 single phase, 208 single phase and 208 three phase, but may not.

Sometimes, some commercial establishments like apartments would be furnished 3 phase power to the building, but metered single phase to each apartment.

What's the power requirement of your product in Watts?

Review the attached diagram and see how 120 volts is dereived from a 120/208 Volt WYE system.

You 120 Volt unit will work fine, your customer basically told you he has a three phase 4 wire system.