Full employment is an idea from economics. It means that every person that is able and willing to work can get a job. It does not mean that all people have a job: People who do not have the skills the employers want may still not have a job, because there simply is no role that fits them. This is called structural unemployment. Also, it is very likely that there will be people looking for jobs (called frictional unemployment).
In general, people say there is full employment, if the percentage of people who are able and willing to work, but who do not have a job is below a given rate. In 1945, William Henry Beveridge said there was full employment if there are more jobs than job seekers. He said that an unemployment rate of three percent of frictional (short term) unemployment can be considered full employment.