Fire away man
Technically, a controller is a MIDI device that sends a signal to a computer program allowing you to manipulate the software. In other words, a controller is like an xbox controller that has certain functions that allow you to "control" music. Basic controllers usually have 2 jogwheels, a few knobs, and a few buttons.
If you've ever touched a record player and moved the record back and forth, that is essentially what a jogwheel does. It allows you to "shift" the music foward, backwards, and scratch. The knobs on a controller are there to adjust effects and equalizers (equalizers cut out certain frequencies). Buttons turn on and off different functions like effects and also playing the track and pausing the track.
Soundcards are either built into the controller or they are external. A sound card allows you to "cue" up the next track by listening to it in your headphones before it goes out to the audience. I recommend the Traktor Audio 2 (http://www.native-instruments.com/#/en/products/dj/traktor-audio-2/)
as it is relatively inexpensive and also includes the Traktor software.
If you were to buy one thing first, I would recommend buying the controller and then if it needed a soundcard buy that. Unfortunately I've never used a controller so I can't give an honest recommendation
Here is a good video of a controller in use. The jogwheels are the big circular things on the left and the right. Ean Golden has a lot going on in his routines so don't worry too much if it looks really complicated, because it is haha.
This is the traktor s2, it is about $500, which is probably too much to spend unless you really want to get into DJ'ing but it has a really clear and basic layout of what most controllers look like on the surface. On top there are the effects knobs and then in the middle there is a mixer which allows you to cross between two (or more!) songs.
Feel free to ask more/ask for clarification