It's important, but it's not a serious as being interrogated by the FBI for a criminal matter. Nevertheless, your testimony can be used at trial or any hearing just like if you were sitting in the witness chair testifying at a trial. Though, some states do have a limitation on whether a deposition can be used or filed as part of a hearing in advance of a trial and those complicated rules are beyond the scope of this outline.
The insurance lawyer or defense lawyer is keenly interested in whether your testimony holds water, is believable, and the biggest mission of the lawyer on the other side of the case is to try to show that you are not a good witness, are a liar, or are not sure about facts that you say support your case. The deposition process is extremely important and valuable to the court system because not only must you as the injured person be believable, but we will take the deposition of the person that caused your injuries or corporate representative of a company that caused your injuries and we are also entitled to show that the "defendant" driver, or company officials cannot be believed or that their conduct was careless. It's an equal opportunity truth seeking device for both the injured person and that person or company being sued for careless or negligent conduct.