In many cases, the defendant pleads guilty or no contest in return for the prosecution's agreement that it will recommend a certain sentence. (See What are the different kinds of plea bargaining?) But with an "open" plea, the defendant pleads guilty without any sentencing assurances.
In many places, "open plea" refers to the defendant pleading without any promise from the prosecution as to what sentence it will recommend. Defendants sometimes reject offers and choose open pleas in the hope that they'll receive a better sentence than they would under the prosecution's proposal.
Another, potentially less risky kind of open plea can arise pursuant to an agreement—where, for example, the parties agree that the prosecution will drop one or more charges, that the defendant will plead to the remaining charge(s), and that the prosecution won't make any sentencing recommendation.
If you want to know about open pleas in your jurisdiction—and want to know whether entering one is a good idea given your circumstances—it's imperative that you talk to an experienced criminal defense lawyer. An attorney with experience in your area should be well suited to explain the law and give you advice. That lawyer may also have, or be able to get, an idea of what kind of sentence the judge would choose if faced with an open plea.