The Mishna on our daf discusses one of the famous “four questions” of the Seder. Here we learn about the first of the two “dippings,” this one is what we call karpas, that is dipped in salt water. The second “dipping” is, of course, the maror, the bitter herbs that are dipped in haroset.
The example that the Gemara uses as the vegetable for karpas is hazeret, a type of bitter herb that can also be used for the maror. The fact that you could, potentially, eat this herb at the beginning of the Seder as an appetizer and then later in the meal as the fulfillment of the mitzva of maror, leads Reish Lakish to conclude that mitzvot tzerihot kavvana – that in order to fulfill a commandment you must have intention to do so (otherwise there would be no need to eat the maror a second time – you would have already fulfilled the mitzva, albeit a little early on, at the beginning of the Seder).
The Gemara rejects this contention: From where do you know that this is the case? Perhaps I can say that actually mitzvot do not require intent. And that which you said, why do I need two dippings, perhaps the reason is so that there should be a conspicuous distinction for the children, which will cause them to inquire into the difference between this night and all others.
The Tosafot Yom Tov explains the oddity in the “double dip” by pointing out that wealthy people eat vegetables during the meal as an appetizer, while poor people eat them before the meal so that they will fill themselves up. Thus, eating vegetables both before and during the meal should provoke questions.
With regard to the question of mitzvot tzerihot kavvana, the Maharam Halava points out that the discussion is whether a person needs to be aware that he is doing a mitzva. No one would obligate a person to think about the deep meaning of the mitzva in order to fulfill it. Rav Hai Ga’on rules that although the conclusion of the Gemara seems to be that a person does not need to have intent in order to fulfill mitzvot, nevertheless a person should do his best to have intent, and he should strive to focus in on the performance of the mitzva to the best of his ability. In fact we find many short prayers that have been established to be said before the performance of a mitzva in order to encourage as high a level of intent as possible.