It is probably a floor drain and is probably there to receive any flooding that might be caused by washing machine, water heater rupture, etc. You didn't mention exactly what was in the utility room but it doesn't really matter because whatever is or isn't in there now may not be what was in there in 1960 when the floor drain was installed. If the water goes down relatively quickly it probably indicates a "slow" drain. This is a drain that is not fully blocked but has reduced capacity to remove waste and therefore sometimes will momentarily back up because it can't handle the normal load. This is often worse when the source of the inflow utilizes any type of pump i.e. dishwasher, washing machine, sometimes but far less often even a disposal. The partial blockage may be caused by any number of things but tree and shrub roots invading the main drain line are usually suspect number one. The first thing you should do is get a professional to come cable your drain. If you can be there do so so that you can see first hand what if anything he retrieves. It may well be worth the money to pay extra for a camera inspection of your line. This will give you a visual on the condition of your main drain. Get a vhs or dvd copy if available so you don't have to guess about what you saw later. Once the line is clear all the way to the main or septic you should start a biologic drain maintenance program. Something like BioSmart. These products are not useful for clearing blockages and should not be used for such. They contain beneficial bacteria and enzymes which will OVER TIME break down ORGANIC material that has built up on the interior walls of your drainage system. They are worth using and don't cost much especially compared to having the line cabled. They will not be effective against tree roots even though tree roots are organic. Tree root growth can be slowed by other means but probably can't be stopped short of killing every tree and shrub within 200' of your drainage system. Ask your plumbing pro what might be available in your area for root retardation. Good luck.