Obviously the thing you put your game disk into in order to install the software on your machine. This hardware is usually located in your tower, although there are also external disk drives. The specifications have to do with the speed in which it transfers the information on the disk to your computer. I haven't paid any attention to this and have never had a problem, however, due to a type of DRM that requires you to play with the disk in the drive, the speed that information is transferred onto your system would account for the requirement. Newer games will use DVD's as they hold more information. Older games on CD's may have as many as 5 discs that need installed. Newer drives will accept both CD and DVD discs. This spec on the label will tell you whether the game needs a CD drive or a DVD drive, which is imperative information as they are not interchangeable. It might also tell you what speed it needs to be. Many people don't install CD drives in their tower anymore and it looks like they may be heading for extinction.
A graphics card is basically another processor with its own memory specifically for processing video images. It thus offloads this work from the CPU (central processing unit) and system RAM. You may hear it referred to as a GPU (graphics processing unit). Graphics cards are also something that can be changed out on your system, but research what people are saying about various makes and models. Games can be optimized for one brand or the other. The game label usually tells you which graphics cards are minimally compatible with the game and occasionally it may not be compatible with specific cards. The problem with this is the variety of graphics cards on the market and the variety of models and series. A game may work better with one brand or another and it's a bit of a guessing game. How do you compare your card to the cards listed under requirements? This is a topic unto itself, so you'll have to investigate your own card by researching it on the Internet. There are sites that compare the performances of various cards. You could also try Can You Run It. Just type in the name of the game.In general, keeping up to date with the latest drivers for your card is usually a good idea, but not always. Sometimes the drivers themselves are buggy and people prefer not to update. Sometimes, just by tweaking some of the performance options ingame you can get it to run better. IMPORTANT !!: any time you are going to install updated software on your computer, create a restore point first in case something goes wrong.
NOTE: My general rule of thumb is "if it ain't broke, don't fix it." You may be buying or updating yourself into bigger problems. Games not running properly are often the fault of the developer and not your system. Sometimes other programs, such as your antivirus, may be interfering with the game and some simple tweaks may fix it, or perhaps you need to update your GPU drivers. When you research the problem, look to people who suggest these simpler solutions first and be wary of advice out of the gate that has you uninstalling and reinstalling your operating system or buying new hardware. These are drastic measures and probably not necessary. Whittle down the easier possibilities first. In my experience, solutions have often come through diligent searching. For instance, some games don't play nice when installed on a different hard drive than Steam, or some don't like Steam Overlay.
HOWEVER, if many people are experiencing similar problems, it's likely the game that's at fault. Fortunately, fellow gamers usually come up with the solutions and often times it can be a very simple fix such as turning Vsync on or off. For a good general overview of getting the best performance from your system and graphics card you can check out Tweakguides
As with graphics, many motherboards come with integrated sound cards. Most people would probably find this sufficient for their needs, but if not, you can also buy separate cards. The typical sound card has a slot available at the back of the computer with various input and output ports and speakers plug directly into this. You can also plug in various external devices such as a digital audio player or microphone. These also have drivers that can be updated.
Although technically your keyboard and mouse are controllers, in the gaming world a controller is a separate hand held device that is used to control all your actions in the game. PC games may or may not support the use of a controller or conversely may play better with one. Sometimes, even though a game is playable on the PC, the keyboard and mouse controls are atrocious and virtually make it unplayable without a controller. Of course, they don't usually tell you that up front, which is why reading reviews first is important. Some games were initially developed for platforms other than the PC, such as Xbox or PlayStation, and don't transition well. These games are referred to as being ported to the PC.