In the legal field, discovery is the exchange of information between parties. In general, it consists of interrogatories, production, and depositions. All of this information is exchanged between all parties to a suit, i.e. between Plaintiff and Defendant, between Plaintiff and 3rd Party Plaintiff, etc.
In most states, discovery is referred to by its corresponding statute in the jurisdiction of the court. For example, in Illinois, interrogatories are pursuant to Illinois Supreme Court Rule 213, production is Supreme Court Rule 214, and so forth. The rule numbers naturally vary from state to state. Each statute explains exactly what information can be requested, and in what format the request may be made.
INTERROGATORIES
Written questions that are sent out and then answered by the other party. These are generally standardized questions asking for specific disclosure. For example, if a lawsuit is brought against McDonalds for coffee burns, an appropriate interrogatory may ask: At what temperature do you brew and store your coffee? These questions must be answered under oath, and objections may be made.
PRODUCTION
Request for the disclosure of physical evidence. For the most part, the request is for the production of documents like medical bills, tax returns, warning labels on equipment, photographs, DNA, black gloves, ...really any physical evidence. All evidence must be shared between parties if a request is made, but if that request is not made, there are ways to keep evidence secret.
DEPOSITIONS
This is virtually the same question and answer session as the written interrogatories, but this is done in person. Witnesses and parties to a lawsuit will be asked to come into an office (or depositions can be taken over the phone, from a jail cell, etc.) where he/she will meet with attorneys involved in the suit. Each attorney will ask questions quite similar to those in the interrogatories, and a court reporter transcribes the meeting. Depositions sound similar to testimony, but it's not a formal session, and no judge or jury is present.
Discovery is how parties exchange information, and it is beneficial to settling out of court. If a case does make its way into a courtroom, discovery affords the parties the privilege of predictable evidence being presented.