It means that if you accept the terms and are a good boy for the required time, their will be no conviction on your record for this.A) What in the world does that mean?
debatable. this is was is called deferred adjudication so there is technically no conviction until then end of the time period. Then, if you can followed the rules, there is no conviction then either. The problem: until the conclusion of the process, there is an open charge on your record.B) Do I need to start checking the convicted of drug possession box on applications?
Not officially but the effect is the same.C) Is this considered probation?
unless they impose some specific rules, this would be equivilant to unsupervised probation where there is no requirement to make reports to a PO. You just keep your ass out of ANY trouble for the year and things go away.D)I live in Michigan, how would probation work?
Not if you fulfill the requirements of the deferred adjudication. It will not be a conviction on your record if you play well with others.E) Can I expect this to ruin my career after graduation?
based on your situation, you were offered the best possibility short of an outright dismissal of charges. I would suggest you accept their offer. If you decide to fight the citation and lose, you will end up with a conviction on your record and based on your facts, you don't have a snowballs chance in Hell of winning.
just make sure (by actual contact with a living breathing person) of any actions you need to take during the deferment period and any actions you might be required to take at the conclusion of the time period to finalize the case.

