Adding a private number plate to a car can make it more personal and although the plate may not mean a lot to anyone else it can represent an important name or date to the owner.
Buying a private plate can be tricky business if you do not know what you are doing, especially if buying it privately from a member of the public. You need to ensure that the plate has been put on retention (removed from the previous vehicle to allow it to be assigned to yours. There is a free to put it on retention and this only lasts for a certain period and then has to be renewed. Some sellers will pay the fee to put it on retention and others will state that the buyer needs to pay this. There will also be a fee to pay when assigning it to a new vehicle.
The process can take a little while and the DVLA may wish to inspect the car that it is going on.