What is it about having multiple coils that enables the magnetic field? Why can't I just have one big wire or threaded wire on a motor? Sorry, it's kind of a baby question but I couldn't find the answer.
It is true that it's only the volume and the power fed to the winding that matters for magnetic field, in electromagnets and motors. Therefore, you could have a single turn winding.
Unfortunately, a single turn would (generally) require a very high current and a very low voltage. This is true on the scales we tend to work at, and the values that physical constants happen to have.
Practical electromagnets use a relatively cheap trick to increase the voltage and decrease the current, by splitting the short fat wire of a single turn into a long thin wire, wound round several times. As each turn has a different voltage, they need to be insulated from each other.
A huge advantage of thin wire in the winding is that connection wires can be a reasonable thickness, and still be much lower resistance than the working winding.
A disadvantage of this trick is that circular wire does not fill 100% of the available area, and the insulation consumes some space as well, so we lose some copper area compared with a single turn. However the trick is so cheap and useful that this inefficiency in area is a small price to pay for the benefits, for almost all applications (in some very big machines, square cross section wire or bar is used for windings to improve the packing density).
Why can't I just have one big wire or threaded wire on a motor?
No problem with this - check out the rotor on most induction motors:
There is no insulation on the aluminium (squirrel) cage and it is, in effect, one shorted turn.
What is it about having multiple coils that enables the magnetic field?
A magnetic field is produced by current AND turns so you can trade turns for current and vice versa. However, if you are interested in making an inductor with particular characteristics then, you need to engineer it by using multiple turns to optimize the inductance for the intended circuit given that there will be limitations on the availability of magnetic core materials.
The reason you need it to be insulated is to ensure that the current goes around each loop when you coil it. If it weren't it could just go "straight". You can have one big wire indeed, but you would need more current to produce the same results.
That is what the number of turns N actually gives in all the magnetic field formulas. It actually lets you have multiples of the current in a given space.
You can do it with a single loop and I have seen this done. However the wires are enormous and must be fabricated in a special way. For instance the wire (more: busbar) is extruded as a wedge cross section, and then rolled in a helix to yield a rectangle cross section.
But the current will be massive. If your input does not lend itself to deliver that kind of current, it won't work.
Magnetic force is amps x the number of turns. You have to carefully calibrate the number of turns and wire size so that it matches your circuit's ability to drive it. Doing it in one turn would require a fairly extreme amount of bucking to get the voltage very low and amps very high.