Ryan,
Your interpretation is correct. Don't overlook the connections themselves. If they are corroded and you scratch the surface down to clean metal with your probe, you're getting an accurate reading of the internal parts. If you just lay the probe on the corroded surface, you're getting a reading including the corroded surface. Make sure all connections are clean.
Steve specified WIRE with no breaks, which should have close to zero ohms of resistance, so he is correct in that aspect. A resistance-type spark plug or coil wire is an exception to this, with a specified amount of resistance per foot of length. Any wire will increase resistance the longer it is, which is why you want to make sure that a long extension cord is sufficient gauge for whatever you're using at the end. Next time you see an extension cord in its original packaging, it should tell you how many amps you can safely draw based on the length of the extension cord. You're not going to run into that problem with any wire length of the proper gauge on a Cub Cadet, with the possible exception of battery positive and negative wires, which seem to be little under-sized in some situations (my opinion).
Ken is partly right when he said that continuity means the circuit is closed which would relate to a voltage path. Assuming the circuit is powered or "live", there would be a needle rise on the VOLTS scale, not the ohm scale. Do not use a meter to check ohms on a live circuit. Zero ohms means there is continuity, which indicates a closed circuit, allowing flow. Infinite ohms indicates an open circuit, which means nothing is getting through at normal voltage.
Ken is probably looking for a blown light bulb about now.....
Roland is right with one possible exception. It's been a while since I used an analog meter, but I believe that instead of no movement of the needle, the needle instead would "peg", showing infinite resistance. Usually on the meters I have used, zero movement indicates zero ohms. Different manufacturers could have set their meters up in different ways. Regardless, the scale will be marked from zero to infinite. When the two probes of the meter are touching each other, the meter should indicate zero ohms, and when they are apart, it should indicate infinite ohms, meaning the circuit is open.