It means that they will be settled using NY law, not that they will be settled in NY. An example might make things clearer.

Suppose a party in the UK enters into a contract with a party in Germany. The contract has a clause that says either party can terminate the contract provided they provide 30 days written notification to the other party. Failure to provide adequate notification can result in some losses for the other party, and so could lead to litigation. The contract has a clause that says it will be governed by the laws of New York State.

The German party wants to cancel the contract, and does so by sending an email to the UK party 31 days before their proposed termination date. The UK party does not see the email for several days, and incurs some losses. They sue the German party in German court. Let's assume that the German party conducts business throughout the world, and so the plaintiff has many choices as to where to sue (they can basically sue anywhere that has personal jurisdiction over the German party).

The key issue is whether or not the German party provided 30 days written notification. Is email "written notification", or does it have to be a more traditional form of written communication, such as postal mail or telegram? Also, 30 days from whose point of view? Does the sender merely have to send the notification 30 days or more before the propose termination date, or does the receiver have to receive it 30 days or more before that date?

Different jurisdictions might have different answers to these questions. If the contract does not define what constitutes 30 days written notification, the outcome can depend on where the plaintiff sues.

What the German court will do is look at their choice of law rules. Those rules will tell them what jurisdiction's contract law to apply when interpreting a contract between a UK party and a German party, and then use that jurisdiction's contract law to figure out what constitutes 30 days written notification. One of Germany's choice of law rules says that if the contract explicitly says what jurisdiction's rules to use, the German court will honor that.

Thus, the German court will try to figure out how New York contract law interprets "30 days written notification". If New York allows email notification, and if the 30 days is from the sender's viewpoint or the recipient's viewpoint.

This is one of the things that makes a judge's job interesting--just because you sit on the bench in Germany doesn't mean you only get to deal with German law. It gets especially interesting if you are trying to apply foreign law to an issue that has not been considered in the foreign jurisdiction. This would happen in this example if New York law had nothing to say about what "30 days written notification" should mean. The German could would then have to try to infer the principles behind New York contract law, and decide what they think would happen if the issue arose in New York.

It is important to note that the German court will NOT use New York law for things not related to contract interpretation. It will use German law for rules of procedure, rules of evidence, qualification of expert witnesses, and things like that.

A completely different thing is a choice of venue clause, although they are often confused with choice of law clauses. A choice of venue clause would say that the parties agree that any litigation over the contract will be brought in New York courts, and that the parties concede that the New York court has personal jurisdiction. You should always be careful if you see a choice of venue clause in a contract, especially if it is a foreign venue for you.

Choice of law clauses are generally pretty safe. They are essentially just shortcuts saving a lot of verbiage in the contract, so that both parties can know what any terms, like "30 day written notice", actually mean.