A witness statement is a statement summarising the oral evidence that a witness will give at trial. The purpose the witness statement is to set out the evidence of the witness; in some jurisdictions the statement will stand as the evidence in chief of the witness (particularly in non-criminal trials), and the trial will simply proceed to cross-examination. In other jurisdictions, the witness statement only serves as a "preview" of the evidence to be given by the witness as part of the discovery process.
Generally speaking, in the United States witness statements are generally eschewed in favour of an extensive discovery process including deposition of key witnesses prior to trial.