Cyclical initiative means that instead of waiting till everybody has gone and then posting the round in a 'begining to end' fashion, you(the DM) post what the NPC's do on their initiative turn, and then PCs post their actions, and once everybody's posted, when you do your update you go from through all the PC's, then end with what the NPC's do again.
EX:
Initiatives:
BOB: 20
NPC: 19
Al: 16
Jane: 9
on the first round, Bob posts his action, you write an update including what bob did, and what the NPC's do. From then on, it's just cyclical.. the PC's post what they do, and you post your updates ending with what the NPC's do next.
It makes it so that the PC's aren't having to tailor their actions in a "If the NPC moves, I follow. If they attack, I attack back. If they stand still I step back and cast a spell, if they delay I delay, etc, etc" way.