To put it as simply as possible, a Cycle is an era of time where things mimic the real world. Cycles are generally 3,000 years long, and are signaled in counting years by the term of (BC) and (AD) with an integer beside it. (ex. AD3 or BC3) The integer to the right of the era is how you can tell which cycle it is. Every Cycle is the same, without being exactly a mirror image of the last cycle. Think of it like a reflection in water, the ripples brought upon by air and other natural occurrences make it distorted. Although you are still looking at a reflection, it doesn't seem exactly like the reflection you would normally see. With each Cycle, the eras get more and more distorted. For example, in the first Cycle, Nazis were defeated almost exactly like they were in the real world; but in the second Cycle, the war ended faster because the United Nations attacked before Nazis made it to Poland. Given say, three more cycles after this one, you might see something like World War 2 never happening, or maybe even the Nazis reigning victorious. The possibilities don't stop anywhere when it comes to this subject.
Each Cycle starts on the 665th of BC, and ends on 2335th AD, no exceptions. This is because the day S.Y.S.T.E.M. was implemented was that exact date of AD, and to make it 3000 years, they used the date of 665 BC.
Another thing about Cycles, is that with the right manipulation from Users, it can distort in a different shape or form. There are Fate Cycles, which are cycles that are distorted naturally and keep a line of laws and orders similar to our real world. Then there are Disrupted Cycles, which are cycles that are distorted by Users, in an attempt to either fix or "disrupt" the natural order of things.
That is all I can share about Cycles at the moment, I hope this bit was informative.