Question: So I have a boss from Ireland that works out of the UK. He tells me that he is on leave for a half term? What is he talking about?

Answer: 
Term as in part of an academic year, more often called semesters in the US, though strictly that only applies to two-term systems and Irish schools tend to use trimesters, though many third-level institutions changed to semesters relatively recently. 

Schools often have a break in the middle of the term, called *half-term*, of which one is coming up soon, the exact time depending on the school. This break is normally relatively short, around a week. 

If you aren't in an academic field yourself, I'd guess that their children will be on a half-term break, and they are taking to be with them.
From the Cambridge English dictionary:
in the UK, a short holiday in the middle of each of the three periods into which the school year is divided <http://dictionary.cambridge.org/dictionary/british/half-term?q=half-term>