A bond is an insurance policy for which the contractor pays a premium. It guarantees that the contractor will meet his obligations in a satisfactory manner. Failure to do so should result in the payment of compensation by the bonding company. There are three types of bonds, payment bond, performance bond and bid bond.
Being bonded could be like getting an insurance policy that the job 1: will be completed and 2: will be done properly. Larger commercial and almost all government jobs will require that all contractors and sub-contractors be Licensed, insured, and bonded. If you can find a bonded electrician you have a good chance the job will be done properly.
One of the problems is depending on the cost of the job, the fees a bonding company charges could be high and this may be passed on to you the customer.
Actually the quality of any good electricians work should be guaranteed until he or she dies. If you do have a problem with faulty work with any bonded contractor, try to get the name of the agent who put out the bond for this particular job.
To get answers to more questions about your electrical system see: Master Electric FAQs