Probatio is a rank/position given to members of Camp Jupiter when you first arrive. After you've completed one year of service (or have completed a valiant task) you are no longer on probation. The equivalent rank in the Ancient Roman legion would have been Tiro/Tirone.
Probation means "proof" when translated to English. Proof that you will be worthy of your cohort, and you are willing to defend and protect your new home. The Ancient Roman Legion equivalent of this rank would be Tiro (pl. Tirones).
Any newly arrived camper is given the rank of probatio and a neck plate with the word on it. Probatio are considered the lowest rank at camp as it is only given to people that haven't been claimed at Camp Jupiter or haven't accomplished some kind of amazing deed.
Frank Zhang was still this rank after a few weeks at camp when Percy arrived. He was charged with cleaning the armory and taking care of Hannibal the elephant, tasks considered beneath the other campers. Percy was also given this rank when Octavian accepted him into the Legion.
Later when deciding a cohort to place Percy in, Frank says that the Fifth Cohort, but because he is only a Probatio, he isn't allowed to represent Percy. Hazel who is a legionnaire steps in and says she will represent Percy instead.
Frank didn't become a centurion until Mars appeared and told him to lead a quest to Alaska. Since only centurions can lead a quest, Reyna was forced to make Frank a centurion. Percy became a praetor from a probatio without being a legionnaire or centurion after helping to defend Camp Jupiter against the Giant Army, as Reyna removed his neck plate and congratulated him on becoming a Praetor.