This Mishnah will list three different opinions of Rabban Gamliel that are more lenient than the Hachamim (the rabbis). The Mishnah says that Rabban Gamliel also said three different rulings that were lenient. Number one: He says that they had couches in those days that they would recline on when they were eating, and there were times when food would fall in. He allowed people to sweep up food from in between these couches, and he wasn't worried that people were going to fill in small cracks in the floor, which would be part of the melacha (prohibited labor) of building. Leveling the floor would have been building. So he wasn't worried that sweeping there was going to cause that. Number two: Umanichin et hamugmar b'yom tov (festival day). You're allowed to burn incense on coals on yom tov. They created a nice smell, even though generally any type of burning is not allowed unless it's ochel nefesh, unless it's for eating purposes. He said that if it adds simchat yom tov (holiday joy), it is permissible. It is allowed. On a deoraita (biblical) level, all types of burning would be problematic unless there's ochel nefesh, unless it was being done for preparation of food. So according to him, burning incense is allowed because once the melacha is allowed for food, he would say mitoch. Since it's allowed for food, it's also allowed for other things that you need on yom tov as well. That was number two.
And number three: Ve'osin gedi mekulas beleilei Pesachim (Passover nights). He allowed people to roast a young goat on Leil Pesach together with the insides, with its innards, like they would do the korban Pesach (Passover offering). Very similar. The korban Pesach was roasted in order to commemorate the korban. He allowed this to be done. Rabban Gamliel, after the times of the Beit HaMikdash, wanted to make sure that when people were having their Leil HaSeder (Seder night), they would remember the korban Pesach.
The Hachamim disagreed with all three of these rulings. The rabbis prohibited these three acts. The first one that we mentioned was mechabedin et hamitot, sweeping up between beds. The Hachamim were worried that it would lead people to filling in different holes elsewhere in the house, and therefore to the problem of le'ashvuye gumot, to smooth out different holes, which is a problem of building. So they didn't allow people to sweep up.
Number two, they forbade people from burning incense on burning coals because they said it's not davar ha-shaveh le'chol nefesh. The Torah tells us that only something that is equally used by everybody, that people usually do, is le'chol nefesh, that most people enjoy this, which is eating. Davar ha-shaveh le'chol nefesh. But when it comes to burning spices of incense, that's not normally done by people, only the mefunakim, only people who are very spoiled, or people who care very much about their physical needs, or people who need a certain smell in the room. So if it's not shaveh le'chol nefesh, it's not allowed to be done. So they disagreed with Rabban Gamliel over there as well.
And then lastly, burning or roasting a young goat was also not allowed for them on Pesach because they said it looks like you're doing the korban Pesach outside of Yerushalayim, which is forbidden. So it looks wrong. It looks bad. So Hachamim said that's also not allowed because we don't want to resemble anything like the korban Pesach.