The controller is potted (i.e. the circuitboard is encased in a resin) and there is a gasket that prevents moisture from getting in to the motor itself where the controller connects with the motor, and all of the wiring connectors are water resistant as well. Which all helps a lot but it is not fully waterproof, and there are highly recommended things you can do to enhance waterproofing, especially if using around saltwater or salted snowy road in the winter.
See below for a picture of the potted controller and the gasket that protects it.
While this is more protection than the vast majority of ebike kits on the market, it is still subject to fluid penetration. System vibration, pulsation and thermal cycling are all common causes of liquid penetrating through a gasket, and water can travel up along a wire through capillary action, especially if there is thermal cycling.
Before installing your motor you should inspect the gasket and tighten the hex bolts around it if needed. Removing the controller and checking the gasket and ideally add some grease or silicone is recommended.
Best approach would be to put a bit of silicone around the gasket (especially where the wiring exits the controller), and put a dab of permatex dielectric grease on each of the connectors before inserting them together in order to make them further waterproofed (note: use proper dielectric grease, not battery terminal protection grease from auto parts stores)
You can also put dielectric grease around the gasket on the controller if you want a more temporary seal instead of silicone or liquid tape. Once the silicone hardens it will need to be cut open, while the grease can simply be wiped off with a rag.
Recommended to use a dab of dielectric grease on every connection and cable that there is, including the battery connections. You don't need to overdo it on HIGO connectors, just use a small amount. This pic has a little too much, just a little grease around the male colored part is sufficient
For your hardcase battery (shark, X1, BABE and etc), you can apply a VERY VERY thin layer of dielectric grease to prevent corrosion. If you can just don't put any where the 2 surface make contact
Depending on what you buy some batteries and displays have USB ports, or other places where water might seep in, for example the places where the battery housing comes together. The USB ports are an obvious weak point so you want those protected at a minimum. No battery is perfectly waterproof so if you are using it in extreme wet conditions you may want to take extra steps such as wrapping pack in a plastic bag.
You could build custom covers for battery/display, and there are an increasingly large number of covers of all shapes and sizes for bike displays on the market, some of which even have a transparent viewing window (google it to see your options). Or you could use silicone along the edges of the housing. For things that are meant to be permanently sealed and not needing to be opened for possible maintenance in the future (i.e. everything but the battery) you can use "Liquid Tape" on the edges of the housing. Also use liquid tape on the wiring exiting the selector switch on the display, if your display is such that the switch is separate from the display. The batteries in particular should be attended to with thoughtful inspection, if it is a hardcase pack, especially the contacts where cradle meets battery case. You can always cover the pack with a plastic bag as well if it is truly pouring down for days on end. (Note saltwater is much more corrosive and should be avoided and/or extra precautionary steps taken to protect pack)
Then you have the throttle and E brakes, the E brakes are pretty durable and should not pose a problem however the throttle is a bit of a weak point because due to the nature of a throttles design it has to be somewhat open and exposed. You can stuff some grease down into it which should help and silicone along the seams that should also help. I would still recommend you have a spare throttle though. Worst-case scenario you just use the pedal assist as a backup until you get replacement throttle wired in.
Then you have the gearsensor cable, and any/all other unused component cable connectors. These should be protected. More grease, cap them off, then tape them off. Take care to do this right and do not leave unused connectors exposed. Note: do NOT put grease into the actual gearsensor mechanism if you are using the gearsensor. But if you are not using the optional gearsensor then you definitely want that exposed plug covered.
It is also important to note that the kind of water is critical. The most troublesome is saltwater such as seawater and snow contaminated with road salt. This sort of thing is to be avoided. Salt and saltwater is much more likely to damage electronics than regular water. This can be protected with the aforementioned grease, as well as protective covers, fenders are a good idea as well.
More info: Electricbike.com: Waterproofing and Troubleshooting
See this link for a further discussion on handling ebike batteries around water
Advanced waterproofing: Spray varnishing BBSHD core