Originally, a centuria consisted of 100 men, just as the name implies. But they were not really a military unit yet, that was the "maniple" (manipulus in Latin, meaning "a hand full"). The maniple originally had 100 men in it (and was thus the same as a centuria), but due to the different equipment and abundance of troops in the main line, they effectively had different strenghts: the front line units (hastati, the lightly equipped, younger/inexperienced soldiers) were often as many as 160 in a maniple, the princeps in the second line numbered mostly around 120 men per maniple, while the triarii (the heavily equipped veterans in the backline) would many times only be 60 or so in a maniple.

From roughly the 2nd century BC on, the maniples were divided into two centuries - this was a matter of command, as the centuries were each commanded by a centurion, with the more experienced centurion being in charge of the whole maniple. With the base number of 160 hastati per maniple, we arrive at the 80 men per centuria.

With the Marian reforms and the abolishment of hastati, princeps and triarii, the base number of 80 men per centuria became the baseline for the whole legion, with the men now being composed of 10 contubernia ("tent communities") of 8 men each. This is comparable to a modern "squad" of soldiers. The maniples were now part of a cohort (which was made up of three maniples/six centuries) and ten cohorts made up a legion. 160 men per maniple gave you around 450 men in a cohort or 4500 men in a legion - the middleground of the planned strength of 3000-6000 legionnaires per legion.

Keep in mind though that these are solely "plan numbers" and were most likely never actually reached in the field.

Source:

DNP (Der Neue Pauly), a German standard lexicon for antique history.