To me and most people it means one of those fighting and adventuring stories you get like Lagan/Naruto/Bleach/One Piece/Dragon Ball/Yuyu Hakusho.
The main protagonist starts out smalll, builds up his power level and goes on endless fights fighting stronger enemies.
Gintama's protagonist, rarely, if not ever does this.
I know Gintama has a few serious arcs every now and then, even so most of the time the plot is silly and involves the everyday lives of the Yorozuya.
That's why I don't like to think of it as a shounen, when its really not.