User summary from Japanese Wikipedia:
A typical "cute'em-up", a horizontal shoot'em-up with a cute fantasy theme and a parody of Gradius. Parodius was originally released for the MSX and is the first in the Parodius series. The goal of the game is to defeat the bugs that eat people's dreams.
The game system is the same as in Gradius, but with the added Bell system from Twinbee. There are five selectable characters, but they all use the same weapon system. The title screen and the stars on each stage are parodies of Gradius 2 for the MSX.
Trivia: It is said that Parodius was a game developed as a stress relief for the staff as the production of "Snatcher" took its time, and that that would be the reason why Parodius contains such weird effects and vulgar graphics. There are many places where the players have to resort to strange methods to even advance through the stages.
Source: Wikipedia, "パロディウス," available under the CC-BY-SA License.