This halacha is not as straightforward as it seems, for there is a dispute brought in the Gemoro (Sukkah 11b) exactly which sukka in the desert our sukka commemorates. One opinion is to remember the Ananei hakovod, the Clouds of Glory that protected us for forty years. (There were seven Clouds, one on each side, one above, one below, and one leading in front; this is why Sukkos is seven days.) Bach adds that the Sukka also recalls the whole event of the Exodus. The second opinion brought in the Gemoro is that our Sukka recollects the temporary huts the Jews built when they encamped. (The fact that the Ananei hakovod sheltered us in the desert is undisputed, this opinion just alludes from the wording of the verse that sukka commemorates the huts, not the Ananei hakovod.) The obvious question on this opinion is what is the point of remembering regular, ordinary huts?

Sefarim explain that the huts remind us that our sojourn in this world is only temporary. Just as nomads in the desert erect tents because they're constantly on the move, so too we don't need deluxe accommodation in this world, as it's only a corridor for the next world. Taz (625) answers that by reliving the experience in the huts we are actually commemorating the episode of the Exodus.

Rashbam (Vayikra 23:43) offers another solution. In the good times we must recall the bad times, thereby reinforcing the idea that Hashem has given us the wealth, and it hasn't come by our own hand. For this reason, Sukkos is celebrated in the harvesting season, to underscore that all our abundance is from Hashem. Rambam in Moreh Nevuchim also answers like Rashbam, adding that this is why we leave the sukka on Shemini Atzeres, since the halacha of rejoicing on Yom Tov cannot be completely fulfilled in the temporary, shaky hut.

The story is told of a poor man who one day made it rich. He led an affluent, carefree lifestyle. But he had one peculiar habit. Every day he would disappear for an hour and no one had any idea of his whereabouts. Finally, someone follows him one day surreptitiously as he makes his way through his palatial home, down corridors, up stairways, through room after room, until he arrives at a locked door in a distant, unused corner of the house, and lets himself in. The person following peeks through the keyhole and watches as the man enters a decrepit log cabin, built into the house. The rich man removes grimy overalls hanging from a peg on the wall and puts them on instead of his fancy clothing. He then seats himself at a rickety wooden table, and sits deep in thought for some time. Later, the fellow confronts the magnate about the strange room and the odd behaviour, and the man replies, "This is the cabin I used to live in and the clothing I used to wear before I became rich. Every day I come here and relive my bad times to reflect on how much good Hashem has granted me."

How do we pasken? Mishna Berura (625:1) rules that we should bear in mind two reasons: to recall the Ananei hakovod and to recall the Exodus. If one forgot either or both of the reasons, he has nevertheless fulfilled his mitzva.

And what about someone who forgot to have kavana entirely? In general, Mishna Berura (60:4:10) says that he must redo the mitzva, although without a bracha. However, by sukka, the very fact that he's eaten in the sukka makes it patently obvious that he wishes to do a mitzva, so he is yotzei even without specific intention to be yotzei (Mishna Berura in the name of Chayei Adam). There is also an opinion that by any mitzva involving eating, one is yotzei bidieved even without kavana. However, this leniency could possibly be relevant only on the first night of Sukkos, when eating in a sukka is obligatory, mitzva chiyuvis. During the rest of Sukkos, perhaps one without kavana would not receive credit for the mitzva according to this opinion.

Rav Shlomo Zalman Aurbach zt"l in his Sefer Minchas Shlomo raises the following question. If someone without kavana hasn't done the mitzva of eating in a sukka, well then is he guilty of eating outside the sukka? Or do we say that the lack of kavana only prevents the fulfilment of the mitzva, but since he physically ate in the sukka, he cannot be considered to have transgressed and eaten out of the sukka? This question is relevant even according to the lenient opinions cited above, in a case where he forgot altogether it was Sukkos, or he specifically intended not to fulfil his mitzva, or during the rest of Sukkos as explained.