If you try jumping on a trampoline, you will notice that when you jump up, the trampoline bends and stretches underneath you. It stretches some even if you stand still, but it stretches extra when you jump.
The trampoline is elastic. When it's stretched, you can feel it pulling back towards its normal shape. Thus, just before you jumped, the trampoline was extra stretched and exerted extra force on you, and this is why you went up in the air.
A similar thing happens when you stand on other surfaces, except that the stretching is very minor and we don't usually observe it. When you jump, your legs exert extra force on the ground. That compresses the ground, making it act like a spring. Being stretched further than normal, it exerts a larger-than-normal force on you, and you shoot up into the air. If you stood on a weak table or a thin sheet of ice, it might be strong enough to hold you as you stand still, but when you go to jump, the extra stretching might be too much and break it.
It is not really necessary that the ground act like a spring; this is just what I thought would be easiest to visualize. In fact you could push off water in a fairly similar way. All that matters is that the thing you push off has inertia, so that when you exert a force on it, it also exerts a force on you.
I think this topic may be confusing for students because the ground is doing no work, yet still exerts a force. The ground doesn't have any energy to use to push you up, so it may seem counterintuitive that the ground is the source of the force. The very word "exert" in the phrase "exert a force" makes us think of actively pushing or pulling like a person does, not sitting there letting things happen to you as the ground does. This is just something you need to get used to. Although in everyday language, we say "I forced the door open" or "I was forced against my will" and the word "force" refers to something that is moving or expending energy or exhibiting some sort of agency, that is not so in physics. The energy to jump comes from your legs (and other parts of your body), but the force comes from the ground.
A similar confusion often arises when students think about the force pushing forward a car driving at a constant speed on the road. Because wind resistance is slowing the car down, something must be pushing it forward to cancel that. Most students will say this is the "force of the engine". But in fact the force that pushes the car forward is the force of friction from the road. The engine does provide the energy, but the road provides the force, as you can learn if the road is very slick with ice and unable to provide sufficient friction force to push the car forward.
Your question details ask whether the force is ultimately electromagnetic. Yes, it is, but this is simply because almost every force we encounter in daily life besides that of gravity is electromagnetic. Molecules have complicated forces between and within them due to electromagnetic interactions of their electrons and nuclei. However, understanding macroscopic forces precisely in terms of microscopic ones is generally very difficult.