BoxyBoy is actually a console version
of the puzzle game Sokoban. Genesis and
Gameboy versions were also released around the same time
(named Shove It! and Boxxle
respectively).
The goal is to push boxes into certain spots on the board
(designated by yellow dots). The trick is that you can
only push the boxes forward. However, if you make a mistake
there is a helpful "rewind" feature.
It's a fun puzzle game, and this version has several bells
and whistles that—in my mind—make BoxyBoy
the version to get. Colorful and fun graphics, catchy
music, goofy cut scenes, and different stage "themes"
(America, Egypt, etc.) all add to the presentation.