Graduate jobs are jobs where you will be expected to have a degree in order to work in the position. People will usually go into graduate employment straight from university, when their education is still fresh in their minds. Lots of major companies are now offering training and graduate contracts, so they can secure new talent in the workplace.
Don’t be put off if you think you might not be completely qualified. Often a company will just want to see that you have a degree and have passed it well, usually with a 2:1 or above. They will usually outline what they are looking for in a candidate, so read the job description carefully and use information from this to write your application. If you are offered an interview, make sure you study the job description carefully beforehand. Look into the company and know details of what they do and their wider industry so you can impress with facts.