CDJ
The common name for a player, often permanently installed in clubs, that handles one deck per unit. It loads tracks from a USB stick or a computer and is operated with the jog wheel and the tempo slider. The basic setup is two of them combined with one mixer.
What a CDJ can do
A CDJ is a piece of gear that loads and plays a track and lets you control its speed and playback position by hand. The main controls are LOAD to load a track, PLAY/PAUSE to start and stop, CUE to return to a set point, the tempo slider to change speed, and the jog wheel to move the playback position.
The screen shows the track's waveform, so you can see what is coming next while you play. With hot cues and loops, you can also jump to any point in the track or repeat a section.
Using CDJs in a club
In a club booth, two CDJs set on either side of the mixer is the common layout. The DJ brings a USB stick with their tracks, plugs it into the CDJ, and loads the tracks. The tracks are analyzed in rekordbox beforehand and exported to USB. Information such as hot cues goes along with the export, so you can use the tracks on the night exactly as you prepared them at home.
Button layouts and features differ between models, so it helps to check which model the venue has before you play.
How it differs from a DJ controller
One CDJ is one deck, and it is separate from the mixer. A DJ controller puts two or more decks and a mixer in one unit, and is usually used connected to software on a computer.
With either one, the flow is the same: load a track, match its speed, and swap the sound on the mixer. What differs is where your hands go and whether you need a computer. Many DJs practice on a controller at home and use CDJs at gigs.