It's a mutual fund flavor of share.
A-Shares...usually "no load." B-Shares? Think: olde schoole load-sold shares. And there are deferred sales charge vibe shares, and back-end load shares, and a load of other...loads.
Z-Shares usually refer to shares owned by employees in the money management firm. They carry a "no load, no fee" status...usually. That is, it's good for all investors that the employees of the money management firm running the money feel a deep ownership stake in the investments they are making.
So the fund company understandably wants to make those investments a "no brainer." That's what Z-Shares are about. No-brainers. "Z" as in Zombie.