Contracts have several basic components: who is involved, what your responsibilities are (annual hours, committees, etc…), separation and termination agreements (how much notice you need to give prior to leaving and how much they need to give you if you are to be released), due process clauses (can you be fired and if so, what are your rights), malpractice coverage, and compensation (hourly, annually, benefits, etc…).
While uncommon, agreeing to a non-compete clause could make it illegal to practice in the town you live in if you were to leave that particular hospital.
While there may be parts of the contract that you don’t like, remember that a contract is entered into jointly. While some paragraphs of contracts I’ve learned to live with, others I’ve rewritten. Don’t sign anything you do not fully understand and if you do not have an attending in your residency who helps residents with contracts, it may be worth the time and money to have a contracts lawyer review your contract.