What @dukepaaron is speaking to is a complex and nuanced conversation. It's not the same conversation that non-Jews are having.
This isn't "What is Zionism", etc. it's more complex than that, and it's not really an outside conversation any more than, say what the bounds of one's marriage are. It's not for an outside.
Duke's response that "it's whatever the popular conception is" is a response to emotional exhaustion, not an actual answer.
For a standard answer for what it is, it's this:
"Zionism is the belief that Jews have the right to self-determination in their ancestral homeland."