“Direct” examination refers to a lawyer’s questions of his or her own witness. For example, in a robbery case, the prosecution might call to testify a witness who claims that the defendant is the culprit. The prosecution’s questioning of that witness is direct examination. The defense lawyer’s questioning of the same is cross-examination.
“Redirect” and “recross” examination are just what they sound like—the lawyers’ chances to question the witness again, before that witness finishes testifying. Judges have a great deal of leeway in deciding what kinds of questions to allow on redirect and recross. Generally, though, redirect is designed for clarification of the witness’s testimony on cross or to address any subject matter discussed on cross that wasn’t mentioned on direct. In turn, recross presents an opportunity for the other lawyer to address the subject matter discussed in redirect, particularly anything that’s new.
Judges sometimes allow the lawyers more than two chances at direct and cross-examination. (Thankfully, these chances aren’t called “re-re-direct,” “re-re-cross,” and so on—just “redirect” and “recross”).
Consider the following example: