Plenty of good answers so far, I will try to add to them without confusing you even further.....
In a DCC system, each loco (and, if you wish, each point, signal and other device) has a circuit board installed called a "decoder". You can buy some locos with decoders already installed, but fitting decoders to exisiting non-DCC locos is reasonably starightforward in most cases (some are simple plug-ins, others are more complicated, but that's a whole world of its own).
The "Central Station" or "Command Station" takes the place of your simple analogue DC controller, in that it is connected between your main power supply and the track; some systems have all the controls on the Central Station itself (eg the new Marklin CS2/CS3 system), others have a separate handset controller like the Massoth Navigator, which is linked to the Central Station either by cable or by wireless link. The Central Station is basically a computer as well as a power supply, but don't let that scare you!
The Central Station delivers full voltage to the track all the time, in the form of a VERY fast cycle AC (much faster than household mains AC cycles) - and it transmits information along the track by varying the pulse spacing of the AC, but that is all Arcane Magicks that none of us really need to understand - all you need to know is that it works....
Now, each decoder (let's just consider loco decoders for the moment) has an "address" - that is a user-programmed number, usually of two digits but potentially up to five digits (don't worry about that for now), which identifies that decoder; so let's say you have your Stainz and your Elias tram, and you've installed decoders in both of them. Say you've given your Stainz address "01", and your Elias "02".
If both of your locos are on the track at the same time, under DC power if you turn the controller then both will move. Under DCC, they don't - each will only respond to information sent through the track that is meant for that loco's particular decoder address.
So, if you select address "02" on your controller, and then turn the speed knob, ONLY the Elias tram will move - the Stainz will still get the same signal, but it will ignore it because it is not addressed to its loco address.
You can then LEAVE THE TRAM RUNNING, and select address "01" - you can then tell your Stainz to do something while the Elias is still happily trundling along at the speed you set for it! When you want to take control of the Tram back and stop it, select address "02" again and you have control back, while the Stainz is still doing whatever you told it to. You can, in theory, do this for as many locos as your system has power to run at the same time - and don't worry, there is always a big "EMERGENCY STOP" button that stops everything on the layout dead if you need to, like if you get in a panic about which loco you are driving at that moment!
There is, of course, a lot more to it - but I hope that has helped to make it clearer rather than more confusing..... the most important thing is that usually, it just works; like all the best technology, it does very complicated things in the background so that you get a simple experience of driving your trains and having fun.
Jon.