The Bill of Lading (BOL) is a document that the driver is supposed to fill in at the time of the pick up after checking your vehicle for any pre-existing damages. If he finds any, he notes them down in the BOL and both you and the driver should sign the paper.
When you receive the vehicle at the drop off location you should check the vehicle for any new damages and in case there are any also note them down in the BOL and sign it. Then you should contact the shipping company, they will send you all needed paperwork and help to submit the claim to the carrier’s insurance company. Here the BOL plays the most important role: if you don’t have it or you didn’t fill it out at the time of pick up or drop off, your claim will most likely be rejected. Bill of Lading is a proof that your vehicle got damaged during transportation and not before or after that.