Dotes answer is technically correct, but here is a little more explanation of what is going on, which may help for similar future situations. The key information from the installation instructions is:
- Green or bare copper wire in wall box to Green terminal screw.
- Line Hot wall box wire to terminal screw marked "BK".
- Load/fan wall box wire to terminal screw marked "RD".
- Neutral wall box wire to terminal screw marked "WH".
Green = Ground
This is standard everywhere. But your old switch, as with many old switches, did not have a ground connection. Most (not sure if "all") new switches have a ground screw or ground wire, including this one. If you have a ground wire with each of the cables, connect it to those ground wires with a wire nut. If you do not, then the question is "is your system grounded and, if so, how?" If the wires to the panel are running through metal conduit then it is likely that the metal conduit - and the metal boxes attached to it - are a legitimate part of the grounding system. If that is the case then you can use a grounding screw with a short piece of green or bare wire to connect the switch to the box.
Line Hot = Black
Hot and switched hot wires can be any color except green, white, gray or bare. But black is the most common for a lot of reasons. With a simple switch, it doesn't matter which wire - hot or switched hot - goes on each screw. With a smart switch, including a humidity sensor like this one, it usually does matter. There are a number of ways to figure out which wire is hot, but the simplest is probably to use a non-contact tester to check which wire has power when the switch is turned off.
Load = Red
A load wire, also called switched hot, can be any of the same colors as hot. But to make things a little easier to follow, red is commonly used for switched hot. In your case, the wire is black (the black that isn't hot) and you connect it to the "RD" screw. As Dotes noted, mark the wire with red electrical tape to indicate it is the "red" wire for anyone working on the box in the future.
Neutral = White
Neutral is always gray or white. You may sometimes find an old white that is not neutral. That is because of the way switches sometimes used to be wired with switch loops. In addition, simple switches - the ones that don't have timers, dimmers, humidity sensors, wireless control and other "smarts" - don't use neutral at all, so in the old days there was no need to have neutral in the box, though often (as appears to be your case) it was included anyway since it had to be patched through to the switched device. Fortunately, you are not in one of those other situations, because if you were then you would not have a neutral wire in the box! In fact, code has changed to require a neutral in the box (or the ability to easily add a neutral when needed) specifically to handle smart switches such as your new humidity sensor.
You have neutral whites in the back of the box. They should be wire nutted together. If so, remove the wire nut, add a short white pigtail to connect to the switch and replace the wire nut - or probably better, put on a fresh new wire nut. If the existing white wires are actually one wire and not two wires connected together then this gets more complicated.