Interrogatories are a set of written questions to another party to the case.
They are most often used to get information about the other side's position on the case, and what to expect from their witnesses. They can also be used to request answers to specific questions related to the case.
In most cases, each side can only ask the 7 "Standard Interrogatories" allowed by Rule 33 of the S.C. Rules of Civil Procedure. Each interrogatory must be answered fully unless you have a legal reason not to answer. If you have such a reason, you will need to object in writing and explain why you do not believe you should have to answer that question.
You should be careful when refusing to answer a question, and you should not ignore the interrogatories. The other side could file a motion to compel you to answer anyway, and the court might impose sanctions on you (such as requiring you to pay the other side's attorneys fees) if they do not believe your objections were justified.
You should also be careful when writing your responses because they can be used against you at trial, especially if you say something different. You must respond within 30 days, though you can ask the other side to agree to give you more time to respond. You can also respond that you are still determining the answer to the question.
For more on this subject, see the section on Interrogatories: Beyond the Seven Standard Interrogatories
You should review Rule 33 of the South Carolina Rules of Civil Procedure for more information about Interrogatories, including a list of Standard Interrogatories.