<raises hand> I'm one.
Probie is short for probationary (usually Probationary Firefighter, but the term's used in EMS as well, I believe). Most fire departments and EMS services require new folks to complete a probationary period where they are evaluated by more senior folks before being granted permanent status. In other words, if you screw up significantly during your probationary period, you may be immediately terminated whereas later on there's more of a review process and you might end up with different disciplinary action. Its also a time of on-the-job training and probies generally do a lot of the "grunt work" around the station. Probies are also generally held to a somewhat higher standard, such as calling officers "Sir", "Ma'am" or by rank instead of by first name and being expected to defer to more senior members (such as getting your meal after everyone else gets theirs).
In the fire service, probation is usually a year-long period. On my department, since we're volunteer, this is where the bulk of your training occcurs (there's a 3-6 month trainee period first, but you end up learning the most during the probie year). We have specific training requirements and other items that must be successfully completed before going off probation. Also, in our department, probies are not considered voting members of the department...regular members get to vote on whether trainees move up to probie, on changes to the Rules and Regulations and for the Chief of the Department and the Department Secretary. We also have higher minimums as far as drill, meeting and call attendance. For example, we have to attend at least 50% of all drills while regular members only have to attend 25%, and we have to attend 25% of all calls while regularl members only have to attend 15%.
Some departments have other requirements as well. LAFD, for example, requires probies to serve at three different stations and in different capacities (engine company, truck company, etc.) before being assigned to a permanent station. I think FDNY might do the same, but I'm not sure.
My probationary period is up in December, and I just had my "final" review with my Captain where he basically signed off on all my training and skills requirements (I still need 2 hours of ropes and knots training), so I essentially just have to wait out the next 2 months and then I'll be a regular member.