What does request for dismissal with prejudice in a personal injury civil case mean?

It means the case is dismissed without the ability to reinstate the action at a later time, i.e. file a complaint against the dismissed defendant(s) for the same cause(s) of action involving the same set of facts surrounding the original complaint. If it was dismissed without prejudice and you discover new facts or law that would make the defendant liable, then you could refile your complaint against that defendant.

You are a defendant and YOU had a motion to dismiss filed AGAINST you? Did you file a counterclaim? If so, then the plaintiff is asking the court to cut your counterclaim out of the case. This would make more sense if you were one of two or more defendants, and you were served a courtesy copy from one of the other defendants of the motion that they are filing to dismiss the plaintiff's suit against them (and only against them). It may not inure to your benefit. If this is a personal injury suit and if you have insurance, then your insurer should be providing you with an attorney. If you are uninsured, then you would be wise to consult an attorney in person so you could show him/her the motion and ask whether you have the same grounds for a similar motion. I am a Florida litigator, so I'm not giving you specific CA legal advice. I'm just sharing some thoughts as a personal injury plaintiffs' lawyer. Good luck.

A dismissal with prejudice means the plaintiff may not refile a civil action against you involving the same transactions or occurrences. A dismissal without prejudice means the plaintiff can refile a civil action, but the statute of limitations will be reinstated as if no prior civil action had been filed against you. You should consult with an attorney to discuss the particulars of your matter and for any specific legal advice.