Most TVs come with one or two HDMI slots standard, but to hook up all the components you have, sometimes more slots are needed. There are two ways to get that extra space--through a splitter or through a switch.
An HDMI switch is a small box that uses the HDMI port on your television as the "in." It gives you anywhere from two to five places to plug other components in; you can "switch" between all of them.
Some systems that use HDMI are supposed to run together (for instance, a Blu-ray player and your surround sound). A good rule of thumb is to use the ports you have available on your television itself for any component you will need for more than one system. With a switch, you cannot play more than one of the connected components at the same time.
A splitter takes one line (from your television) and splits it into two, so your components eventually lead back to the same port. It works just like the old coaxial splitters.
The main problem with splitters is that they overload your ports. If you are using both components at once (or, say, you forget to turn one off) your screen may appear jumbled and your television might react. Also, if you are trying to play one component on multiple televisions, there may be a chance the picture will come out jumbled or grainy.
What is Best for You
Depending on your situation, you may benefit more from one than the other. A switch is usually preferable if you are trying to hook up more than one gaming system, because the odds are you will not be using these at the same time. Splitters are usually used when you have more than one TV you would like to send a component to (like using one Blu-ray for two televisions). To prevent overload on your television, most retailers will recommend a switch.