A log book is a colourful piece of paper which has the details of your car (and previous owner should you have one). If you need to sell the car you will need this piece of paper. It is A3 size and folded in half....it should be with your car's paperwork/service history etc. DON'T KEEP IT IN THE CAR!! If someone breaks in, they have all the necessary paperwork to sell the car!

Don't know what country you're in, but in the UK the 'Vehicle Registration Document' is commonly referred to as the log book. You should have received this from the DVLA when you bought the car and the ownership was transferred to you. You'll also need to produce it to MOT the car. Get on to the DVLA if it's lost, as if you're stopped by the police and can't produce it, you could be in trouble.