A notary public is an official appointed position by the Secretary of State's office in a given state. As with most public officials, the State requires that the individual obtain a surety or notary bond prior to receiving their appointment. This bond "makes sure" that if the official violates the public trust through negligence of their duties, funds are available to reimburse the State for its loss.
The primary responsibility of a notary public is to validate that the individual parties to a contract are who they claim to be. The State may suffer a loss if the notary fails to properly confirm the identity of the parties.
Here's an example...
Let's say Jim wants to buy a car currently titled to John. Jim and John bring the title to their local notary public to notarize their signatures on the transfer of title. The notary asks both for their drivers license to confirm their identities. Jim promptly presents his, but John claims to have left his ID at home. John is in a hurry to get the deal done, so the notary public simply instructs both Jim and John to sign the title, after which the notary signs or notarizes their signatures.
Unfortunately the person claiming to be "John" is actually John's roommate Steve. The real John is away on vacation and had no intention of selling the car. Do you think this John is a happy camper? Had the notary refused to witness the transaction because Steve didn't present identification, John would still have the title to his car.
As a public official, the notary public in this example violated the public trust by failing in their duty to confirm identity. John has recourse to file a claim against the State in which the transaction occurred for his loss, because the State was negligent through its appointed representative.
A notary bond is a guarantee of payment to the obligee (the State) should a loss occur for a penalty amount of the bond. Notary bonds are usually provided by a surety company (typically an insurance carrier). The bond generally runs concurrently with the term of the notary public's commission.
You're probably familiar with an auto insurance policy. If you have an auto accident, the insurance company pays the claim and writes off the loss. You aren't required to reimburse the company for the damages.
Unlike an auto insurance policy however, a notary bond is simply a guarantee that the funds will be available should a loss occur. The surety (insurance company) makes a payment to the State up to the penalty amount of the bond. However, this loss paid by the surety is not simply written off. They will most likely seek reimbursement from the bonded party - the NOTARY!
A notary bond protects the public. Who protects the notary? Insurance coverage is available to provide this protection - it's called Notary Public Errors and Omissions and may be purchased for a nominal fee from insurance companies.
To sum up, purchasing a notary bond is a requirement to become a notary public. I hope this overview has shed some light on why this is needed to protect the public trust.