Almost everything on a laptop is fragile, and vulnerable to damage from knocks and drops. However there are two components in particular that are more likely than others to suffer damage if a laptop is dropped, and hence these are the most likely to need replacement at some time during your laptop's life.
A laptop computer contains basically the same components, or variations on the same components as a desktop computer. On the whole they are smaller and require less battery power but they do the same job. The thing that makes them really different is the fact that a desktop computer sits on a desktop and is rarely-if ever moved, where as a laptop is moved frequently from place to place. Worse, it is used on a person's lap or on a raised surface such as a desk or stool where a knock may cause it to fall several feet.
The hard drive in the laptop can be damaged during either a fall or when a laptop suffers a hard knock. When this happens the head that reads the data from the disc can crash down onto it, damaging the surface of the disc and making it unusable in that area. This will lose the data in that sector, and if bad enough can put the disc out of operation entirely. Solid state drives have no moving parts and hence are not vulnerable to this kind of damage.
The LCD screen is the other part most likely to break, and unfortunately it is the most expensive single component in the laptop. When it breaks, the liquid crystal drains from where it should be and you may initially find that you have a patch or stripe that goes black. Eventually the whole screen will fail, if it doesn't initially. Other failures to the screen may leave lines or patches of white on them, but ultimately the result is the same as it will need to be replaced.
Screens can be bought online for far more reasonable prices than a computer repair company will charge you. Fitting them is more often than not an easy process that requires that you remove a few parts from the case, such as the bezel. The old screen will have to be disconnected first as there are normally a number of cables that connect it to the computer, and these may even go under the keyboard.
A few basic tools such as a small, magnetized screwdriver will be needed, sometimes with a torx head on it. Once the old screen is removed, putting the new one in place is simply a case of reversing the process-first plugging the screen back in, then replacing the keyboard, screen hinges and bezel and anything else that may have been removed. Tutorial videos can often be found online for specific laptop models.
There are of course other components that may be damaged when a laptop is dropped, including the motherboard and any of the components that are soldered onto the printed circuit board such as the charging pin. These however tend to be bigger repairs, requiring specialist tools and are not so suited to DIY repair.