Printed instructions for my new electric cooktop say: A 3-wire or 4-wire, single phase, 120/240 volt, 60-Hz., AC only electrical supply is required on a separate, 40-amp circuit fused on both sides of the line. Obviously there are breakers in the breaker box, but what does "40-amp circuit fused on both sides of the line" mean? Thanks!
I believe the simplest way to put it is, it needs to be on a dedicated 40 amp double pole breaker.
With a 240 volt appliances there are 2 "hot" lines, usually a red insulated wire and black insulated wire. A neutral, usually a white insulated wire, and a ground wire can be bare wire or sometimes insulated in a green covering.
The 4 wire connection is the accepted code compliant connection, the 3 wire has been phased out, but still does exist in older connections.
I hope this gets the idea across. There are a few well versed electrical guys on SE that really know the ropes well when it comes to electrical issues. They may be able to fill you in a little more.
They're packing a lot of information in one sentence.
They're making a distinction between 3-phase (like New York City and Brazil) and split-phase (everywhere else in 120V-land). Split-phase is really just single-phase, with a tap in the middle. The middle tap goes to neutral, and since neutral is supposed to be near ground potential, we usually don't bother putting circuit breakers on it.
So they are telling you that both hot wires need a circuit breaker. That is also to deter you from hooking it up 240V-only (no neutral) or Euro-style 240V (neutral at one end, where you would normally only breaker the non-neutral).
By saying "120/240V", they are saying the oven requires neutral be in the middle. Typically ovens use neutral for 120V loads, which are trivial: clock, controls, ignitors and the oven light. Incandescent bulbs s are as happy at 500F as Br'er Rabbit is in the briar patch, so bringing 120V out to an oven lets you use any dirt-common 120V incandescent bulb, instead of having to hit up Batteries-n-Bulbs for a weird 240V bulb. For this reason they bring neutral to ovens.
By saying 3- or 4-wire, they are saying they don't care if there's a ground. However, Code cares if there's a ground. Prior to 1989 (??) you could wire an oven with hot-hot-neutral no ground. (not alright was wiring it with 8/2 NM cable with bare neutral; the only bare neutral ever allowed was SE type: strands wrapped around conductors). They are saying if your house doesn't have a ground wire, they can accommodate that.
What they do is ground the oven to neutral. Which is awesome until the neutral breaks, then, opening the oven door causes the chassis of the oven to be electrified at 120V. But hey, at least you don't have to search for a 240V bulb!