First off, NAC stands for Notification Appliance Circuit. This is the circuit that powers the horns, strobes, chimes, and speakers in a building. This is the circuit that notifies the occupants of a fire. Usually, there is more than one NAC circuit from the fire alarm panel.
Connecting all the horns and strobes on the circuit in a daisy-chain fashion like a single strand bead necklace, the NAC circuit is loop of wire. To allow a small current to be passed through all the wires, at the end of the daisy-chain is an end-of-line resistor.
This current is supervision current, which is another term for continuity checking. The panel is checking the continuity of the wire in the loop.
An open trouble on the NAC says that the supervision current has stopped flowing and the panel is not seeing a continuous wire path (broken continuity).
If the current stops flowing through the circuit, it's because of a loose connection or a broken wire. The panel has to pay attention to the current because if the current stops, it means that some or all of the horns and strobes on the circuit won't receive power. Basically, some people won't know about a fire in the building until the smoke reaches them.
Your job is to find the broken wire or loose connection and fix it. Keep in mind that all possibilities need to be looked at until the problem is fixed, and this open wire could be a bad splice in the wire somewhere, an actual broken wire, a loose screw connection on a horn or strobe, or even a minihorn inside an apartment that has been removed by the resident. If it's a removed minihorn, you'll need access to the apartments to find this.
Usually there more than one NAC circuit out of the fire alarm panel, and if the panel is showing that there is an open circuit, it shows which circuit is having the problem. Once you've figured out which circuit and where the circuit runs in the building, you've narrowed down where to look for the problem.