Depending on what we mean by “background,” there are at least two reasons why this is important.
First, the “background” of the testimony might refer to the events that surrounded the things to which the witness is testifying. In that case, understanding the background is important because it helps an investigator know how plausible the witness’s statement is and it helps them to know what to ask the witness. For example, if you are interviewing an eyewitness who claims to have seen the aftermath of an armed robbery, it is important to know all the facts that you can about the robbery. That way, if the witness’s testimony seems to contradict what you already know, you can follow up on contradictions.
Second, the “background” of the testimony might refer to the witness’s personal background. In that case, understanding the background is important because it might give you some clues as to how the witness might be biased. For example, if the witness is in some way connected to the victim of the crime, or to the person who is suspected of committing it, their testimony might be suspect.
For these reasons, it is important to know the background of the testimony.