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. (See What does it mean to "plead to the sheet"?)
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. (See Can you reach a plea bargain with the prosecution without agreeing on a sentence?)
Example: The prosecution charges Nicky with driving on a suspended or revoked license with an enhancement for being a habitual traffic offender. The prosecution offers her a plea bargain by which she would receive a 180-day jail sentence in exchange for a guilty plea; the trial judge seems willing to issue this sentence. Nicky, however, is hoping for no jail, so she decides to plead "open" to the court. The judge advises her of her options: accepting the state's offer, going to trial, or pleading open. The judge also explains that, with an open plea to this offense, the sentence could by anything from no jail time to five years in prison. Nicky chooses to go with the open plea. The judge then sentences her to three years in prison. (Hornbuckle v. State, 864 So. 2d 1203 (Fla. Dist. Ct. App. 2004).)
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.