The plot of the game refers to feudal Japan being given giant mecha, the player being the pilot of one such mecha, the Aleste, fighting against the other feudal lords. In the game itself the plot is not referred to at all.
Robo Aleste follows the traditional vertically scrolling shooter style, with the player flying forward and enemies coming from the front, sides, and rear. At the end of each level is a boss, which the player must defeat in order to move on. Each boss is one of the warlords allied against Nobunaga. Like most scrolling shooters, there are several weapons which can be collected and powered up.
Source: Wikipedia, "Robo Aleste", available under the CC-BY-SA License.