Hi Zuv - a skimmer is not an ABSOLUTE MUST, but, it does help that you can keep more challenging species of fish, anemone's and corals. A decent skimmer is also a "fail-safe" mechanism, to ensure that you don't loose ALL your lifestock, IF one fish decide to die in the night, and you don't know about it.....
You can still keep a successful marine aquarium, BUT, you WILL have to compensate for the lack of a decent sized skimmer.
You can compensate, by doing one of the following:
1) do water changes more often
2) create / add an algae scrubber - seach MASA for ATS or algae scrubber
3) feed less
4) keep less fish
The cycle being referred to, is the denitrification cycle. That is the process where the natural bacteria filtration of the tank, goes through the motions of getting the tank's water parameters, and nutrient levels, as low as can be, and also, as stable as can be.
Once these 0 (zero) levels, or ultra low levels have been reached, due to the working of the bacteria, then you can start adding lifestock.