It would be great if an electrician with years of experience could answer your question. Alas, you are stuck with me, for now. When I don't know the answer I do a search. Sometimes my search gets me good info. This LINK may be helpful. Scroll down to Comments and see Kaj Carlson's brief history of wiring and fuses.

I think you have a 60 amp service. The 40 amp fuse may handle a water heater or electric dryer. The other fuses are for general lighting and outlets. I grew up in a home built in 1950 that had a fuse box and very basic electric service. In fact, there were no ground wires to any of the outlets. After the house was sold, it was remodeled with the wiring upgraded to meet current code.

JuneKnow knows. I moved into my house (built in 1955) in 1967. It had just what you describe. The 60A was the main, and a 40A fed the kitchen range. There were four Edison base fuses. It also had an add-on outrigger box for a dryer cable. This wasn't even sufficient in the '60s, so I started upgrading as needed.

As of today I have two main 200A breaker panels, and two 100A auxiliary breaker panels in an addition. I also have a small panel allocated to load reduction when the generator is running. The cable to the dryer, one of several grounding conductors, and part of the garage lighting circuit are the only parts of the original system still intact, including the connection the the utility pole, drop, meter and meter box, transfer switch box, and SE cables.

To answer the original question: The 'service' is whatever the power company claims it is, as they have their own rules separate from the National Electrical Code. However, the most you can draw from that box is 60A. And I would wager that most of the household circuits are on one fuse, and most of the lighting is on another. This makes repairs a big deal as much of the household electricity has to be shut down.

[Edit: Also, there are rules that limit actual current draw to around 80% of the circuit rating for continuous use. That would make your effective current supply 48A. A modern electric kitchen might be able to exceed that by itself. Throw in a dryer, air conditioning, pool heating, etc., and it may be obvious that an upgrade is called for unless very low energy living is envisioned. Use of an electrician is advised to help you determine the scope of work. Otherwise, a careful reading of much of NFPA 70 (the NEC) will be needed. I recommend the "Handbook" version for clarity.]