If your resistor is of greater resistance than the threshold on your meter, then even though current can flow through it, the meter will not register continuity. The continuity test applies a very small voltage to the circuit and check what current flows through it.

How do you know if a resistor is bad?

Set a digital multimeter for "ohms." Set an ohms range that is equal to or higher than the value of the resistor to be tested. Touch the red lead from the meter to one side, and the black lead to the other. Resistors do not hold a polarity, so it doesn't matter which side gets the red or black lead.

Does resistance mean continuity?

Think of it this way: Continuity is a binary version of resistance. If the resistance of the thing we're testing—the wire we want to make sure isn't broken, the connection we want to be certain actually goes to ground, the switch we want to know works—is low (like less than 1 ohm), we say that it has continuity.