It means a definite commitment to have work/a contract. If something is 'legally binding' it means to the two parties are committed and cannot change their minds (they are metaphorically 'tied together').

"Binding job offer" means a job offer that is formal and official, where the employer is bound to give you the job. So, for example, if the company gives you a formal job offer letter and asks you to sign and send back, that may be considered a binding job offer. They may require something even more formal, such a legally binding contract for a job. It may depend on the country.