Tosfot Pesachim 105a והנ"מ, based on a Midrash Tehillim, mentions that in their time they were very strict not to drink water after mincha on Shabbos, and as a gezeira, not to eat a meal during that time either. The Rosh (beginning siman 13) says that the minhag was not to learn then either, because Moshe died on Shabbos afternoon.
The mesivta gemara gives more details, and explains why we don't follow these practices anymore. (Although apparently there is still a limited version of this minhag Drinking Water During "Shalosh Seudos").
If the paytan did follow them, maybe this is what he was referring to. They could presumably take walks or have non-Torah conversations, but at least in some situations (raining, people who live alone, ...) there may not have been much for people to do other than sit and wait. So it's a praise of Klal Yisrael that they followed their minhag and just waited around.