Logbook loans are a way of borrowing money, secured against your car. It is called a logbook loan because you will hand over the V5c registration document for your vehicle (also called the Logbook).
During the terms of the loan you can continue using the car, but if you fail to make the repayments your car will be taken away and sold.
Logbook loans are an extremely expensive way to borrow with interest rates often being around 300% APR, meaning you can often repay double what you received from the loan. They are often taken out by people who are already struggling with their finances.