1 interpret, define, explicate, detail, delineate, make plain, simplify, spell out, resolve, get across, clarify, clear up, elucidate, illustrate, expound, describe, disclose, unfold, unravel, untangle:
The teacher explained the theory so that even I could understand it.
2 Also, explain away. justify, account for, excuse, rationalize, legitimate, legitimatize, extenuate, palliate:
You will be required to explain your absence.