The term ‘obligee’ is one that pretty much always trips people up the first time they hear it.
In terms of surety, the obligee is generally a state government agency.
Basically, it works like this:
Your client (known as the ‘principal’) is obligated to perform their duties (live up to their side of the bargain) through a contract (known as a ‘surety bond’), with a specific agency within your state government (the ‘obligee’) acting as the enforcer of the contract.
In practical terms, it means that if your client screws up, the person who hired your client will let you know that they failed in their duties, and that you have to cover their failures financially up to the limit of the surety contract.
From there, you have the fun task of letting the government agency know that you had to financially cover for your client’s mistake (the principal), and that they are now obligated to pay you back, with the government backing you up.
The obligee is the 800 lb. gorilla on your side.