I'll explain the first stanza here. Hopefully, having the first few lines explained will give some context and help explain the rest of the poem. Also, remember that you can always look up individual words that you find strange or confusing because they often have secondary, archaic meanings.
"Laugh and be merry, remember, better the world with a song": Remember that the "song" of laughter and happiness will make the world a better place. It's implied here that happiness is more helpful to the world than sadness or negativity.
"Better the world with a blow in the teeth of a wrong": The world is a better place when justice is served to those who have done wrong. This line relates to the first and implies that laughter and happiness are ways to seek justice.
"Laugh, for the time is brief, a thread the length of a span": Laugh because our lives are very short, like threads that are merely the length of a span, which can mean either a very short period of time, or the arch or part of a bridge that extends between its supports.
"Laugh and be proud to belong to the old proud pageant of man": Laugh (again—this poem thinks that laughter is really important!), and remember that you belong to all of humanity. This line perhaps encourages the reader to look at the big picture—life isn't just about you, or any one person, but all of humanity and history.