What is zero unemployment?
I have changed your question to read "zero unemployment" because I have never heard of the term "zero employment" and because zero employment (no one working in the whole economy) would really be impossible. Zero unemployment, on the other hand, is a term that is used in economics.
Zero unemployment refers to a case in which the unemployment rate is zero. Please do not confuse this with a case in which every single person in the economy is working. That is not what unemployment means.
A person is unemployed if he or she wants a job and cannot find one. The person is not unemployed if they do not want a job -- if they are retired, for example, or if they stay home and take care of their kids.
So zero unemployment occurs when there is no one in an economy who wants a job and is unable to find one.
Unemployment in economics and in economic policies refers to only such cases where people actively looking for work are unable to find employment. This means that people who are out of work for certain specified reasons such as transition from an old job to a new one, retired people, and people who are on holiday or for some other reasons do not wish to work at a particular time, are not considered as unemployed.
Different countries and economies may use different criteria and method for identifying the unemployed. Accordingly the exact definition of the unemployment may differ to some extent from country to country.
It is important that no country has zero unemployment rate in practice. Generally an unemployment rate of 3 to 4 percent is considered quite normal for countries with good economic health.