Karel-
There are a lot of great keyboards out there. For anyone to give you good advice I think we need more information.
Budget? Can you give us SOME idea how much you're willing to spend? A ballpark figure at least.
Your options are keyboard workstations like the Motif, Fantom and Triton; a separate controller keyboard and either modules or soft-synths on your computer or; you could consider getting something used. All the workstations sound good and all are available in several configurations with a range of prices. A separate controller and modules might make sense if you got something used. That would keep costs down. Soft-synths are also generally less expensive than their hardware counterparts. In fact, there are a lot of free VST and DX instruments out there.
If keyboard feel is important to you (and it should be), then you'll need to play as many different keyboards as you can before you can begin to narrow the field.
Sorry to be so vague, but there are a lot of keyboards out there.
MIDI- Musical Instrument Digital Interface
This has been covered countless times. I'll give you a quick answer, but if you take the time to do a search here or on Google, you will find a wealth of information.
MIDI was developed in the early 80's because, before then, each manufacturer used a different, proprietary method for communications between various pieces of equipment. Essentially, if you bought an Oberheim sequencer it would only work with an Oberheim synth. It became clear that digital was the direction things were headed so the manufacturers agreed on a set of instructions to define the various aspects of a performance. This then allowed any device with a MIDI implementation to work with any other device with MIDI.
The key thing to understand (and what always seems to confuse people) is that MIDI is NOT audio. MIDI describes a performance. It tells a synth, for instance, to play a specific note at a specific time for a specific duration. The synth, interprets these instructions and produces the audio you hear. Because MIDI is not the actual audio, MIDI files are many times smaller than the audio files produced from the performance. This makes MIDI ideal for use online and for transferring files between different places. The downside is that different synths will produce different results.
Because MIDI is very flexible, MIDI can also be used to do other things than produce sound. This is why some digital mixers and lighting controls can be controlled via MIDI.
This is a VERY brief description of what MIDI is. Do a little research and you will find more in depth information. MIDI can be confusing at times, but it's proven to be very robust. Its adoption over 20 years ago truly changed the face of contemporary music.
Ted