To be clear. Right now the 3 main "protocol" to move visual information trough a cable are :
VGA : The old analog format, used a lot in CRT (big screens from the 90's). Also still used by lots of modern LCD screen, even tough the format have some limitations.
DVI : The more recent numeric format. Almost all LCD today support it, and all modern graphic card support this. Also, The DVI format in itself generally include connectors to transport VGA signal. That's why its so easy and cheap to build a DVI to VGA adapter. Also, DVI is the signal used by HDMI, who is a connector that include DVI and Sound information. Thats also why its easy to find a DVI to HDMI adapter (or vice versa).
Display Port : A more recent than DVI format, who can transport more information and thus can support higher resolution than DVI. Apple use this format for their computer.
BUT, what is important to understand is that its not only the form of the connectors, its the way data travels trough cables, its way more complicated than just the connector. With the right adapters you can travel DVI and VGA signal trough a Display Port connector. The iMac graphic card support Output for VGA and DVI, so you can use adapters.
However, the DP on the iMac 27 support input, but the input goes directly to the display and there is no scaler or processor that can convert DVI or VGA to the Display Port langage the display need. So basically it only accept Display Port signal trough Input. also it only support resolution that doesn't need computation for the display, like native 2560x1440 and the exact half 1280x720 (720p).
So, your computer need to have a graphic card that can output Display Port signal. The iMac display won't be able to use a DVI or VGA signal.
An "active adapter" is more than just a connector, it's like a little external GPU that will accept DVI or VGA signal and translate it to Display Port signal on its output. So it is way more expensive than a regular adapter that just enable a DVI connector to connect to a Display Port connector. The Active Adapter is really a computer itself.