To fall over (often in a dramatic or comical way); colloquially can also mean to flop or fail badly.
雨の日に道で滑ってすっ転んだ。
I slipped on the road on a rainy day and fell flat.
舞台で転んで、観客の前ですっ転んだコメディアンが笑いを取った。
A comedian fell on stage and got laughs by falling flat in front of the audience.
彼の発言は場にそぐわず、すっ転んでしまった。
His remark was inappropriate for the situation and he ended up embarrassing himself.