As noted, the Sages ordained eating a vegetable dipped in liquid between kiddush and the recitation of the Hagada in order to change routine; all year long, we eat vegetables during the meal, after washing hands over bread, but at the Seder we eat a bit of vegetable before reciting the Hagada and before washing hands for the meal. Two things are unusual about this: first, we eat a vegetable before the meal, and second, we wash our hands twice instead of once (Rashi and Rashbam on Pesachim 114a; Tur §473). In addition, by eating a vegetable before reciting the Hagada, our Seder meal obtains added importance, because the finest banquets generally begin with appetizers and hors d’oeuvre, followed by a pause for a different part of the program, after which the main meal begins (based on Bach).
The word “karpas” appears neither in the Mishna nor in the Talmud; we are only told that a vegetable is eaten before the Hagada is recited (Pesachim 114-115). But a few Rishonim (Maharil, Raavan) write that karpas should be used, because its Hebrew name alludes to the 600,000 men put to hard labor in Egypt (the Hebrew letters of the word karpas can be rearranged to spell “samekh parekh”; the letter samekh has a numerical value of sixty or 600,000, and parekh means hard labor). Though not mandatory, the Acharonim say that it is good to use karpas (SA 473:6, MB 19 and Kaf Ha-chayim 49 ad loc.). However, there are differing opinions about what karpas is. Some say it is celery, and this is the widespread custom among Sephardim. Others say it is parsley, which is the custom of some Ashkenazim. Most Ashkenazim, however, use neither celery nor parsley, because there is uncertainty about what blessing to recite over them in the Ashkenazic custom. They instead use boiled potatoes. Each family should continue its own tradition.
We dip the karpas in salt water or vinegar and recite the berakha of “borei pri ha-adama” (Who creates the food of the soil) with the intention that it also apply to the maror that will be eaten later in the meal. It is not necessary to recline while eating karpas because some poskim say it alludes to the suffering of enslavement in Egypt, and therefore need not be eaten as a demonstration of freedom.
One must eat less than a kezayit of karpas. Though some Rishonim (Rambam) say that more than a kezayit of karpas should be eaten, it is best to avoid this, because eating more than a kezayit invites uncertainty about making a berakha achrona, since according to Ri, a berakha achrona is necessary, but according to Rashbam, one should not recite a berakha achrona, because the blessing over the karpas covers the maror we eat during the meal. Therefore, as said, it is best not to eat a kezayit of karpas. If one eats more than a kezayit of karpas, he should not recite a berakha achrona, because we rule leniently whenever there is uncertainty about reciting a berakha (Maharil; SA 473:6).
 See Mikra’ei Kodesh pp. 184-187 and Sidur Pesach Ke-hilkhato 2:5:3 regarding the opinions and customs of eating karpas. In general, the advantage of eating celery or parsley, in addition to the fact that they are actually karpas, is that they are eaten raw and stimulate the appetite. Moreover, they are usually eaten in small amounts, which makes it easier to eat less than a kezayit, as will be explained below. On the other hand, in Ashkenazic communities they were not generally eaten raw, and consequently one who eats them raw should recite the berakha of “she-hakol”. But the berakha on karpas must be “ha-adama”. Therefore, the custom in Ashkenazic communities is to eat cooked potatoes for karpas, on which the berakha is undoubtedly “ha-adama”. In Middle Eastern and North African communities, where celery and parsley were eaten raw, one recites “ha-adama” over them.
It is worth adding that one should not use any food for karpas that normally eaten outside the context of a meal – bananas and pineapples, for example – since it is not clear that they are being used as appetizers; rather, they look like separate foods that are eaten by themselves, do not seem different, and do not provoke questions. Vegetables, however, are usually eaten in the middle of the meal, so eating them before the meal is a change.
 This dispute hinges on whether one must recite a berakha on the maror. According to Rashbam, a berakha is necessary, since the berakha of “ha-motzi” over the matza covers everything that will be eaten during the meal, meaning anything that is eaten with matza to provide satisfaction. But maror is not eaten for this purpose, so it is not covered by the berakha of ha-motzi. Therefore, one must have in mind when making the berakha on the karpas to cover the maror as well. By doing this, he exempts himself from making a separate berakha on the maror. However, according to Ri, one need not make a berakha on maror at all, since it is considered a food that is eaten in context of the meal and hence is covered by the berakha on the matza. Accordingly, if one eats more than a kezayit of karpas, he must recite a berakha achrona. He should not wait until Birkat Ha-mazon, since it only covers food that was eaten during the meal, not before it. So if one eats a kezayit of karpas and does not recite a berakha achrona right away, he misses his opportunity to make the berakha.
Nevertheless, be-di’avad, if one ate more than a kezayit of karpas, he should not recite a berakha achrona. This is because we are lenient in laws of berakhot in cases of uncertainty. On the one hand, perhaps the Rashbam is correct that the berakha on the karpas covers the maror, and since Birkat Ha-mazon covers the maror, it also covers the karpas, which is connected to the maror (see BHL 473:6, which cites Gra that one must make a berakha and concludes that the matter must be explored further. Nevertheless, practically speaking, one should not recite a berakha that is in doubt). On the other hand, if one ate a kezayit and recited a berakha achrona afterward, he should not recite a berakha on the maror, since perhaps Ri is correct that the berakha on the matza covers the maror.
If it is true that one must eat less than a kezayit of karpas, why is one required to wash his hands? We know (SA 158:3; Peninei Halakha, Berakhot 2:6) that one only needs to wash hands for a piece of bread larger than a kezayit – kal va-chomer that one need not wash for a food dipped in liquid. Indeed, according to Rambam (MT Laws of Chametz and Matza 8:2) and many other Rishonim, one should specifically eat a kezayit of karpas (in a responsum he instructed his correspondent to recite a berakha achrona afterwards). This was in fact the practice of the Vilna Gaon and several other Acharonim (although it is unknown whether they recited a berakha achrona afterwards). BHL 473:6 leaves this issue unresolved. Perhaps according to Netziv (cited above in n. 12), who says that we wash our hands before karpas to remember what used to be done in the Temple, we can suggest that in the times of the Temple people would eat pieces larger than a kezayit, and they knew whether or not to recite a berakha achrona. Nowadays, however, since we do not know whether to recite a berakha achrona, we eat less than a kezayit to avoid uncertainty, and although technically we need not wash our hands to eat less than a kezayit, we do so anyway to commemorate what was done in the Temple. See also Kaf Ha-chayim 158:20, which states that there are some who learned from the status of karpas that the law of washing for vegetables is different than the law of washing for bread: for bread one only washes for a kezayit, but for vegetables one washes even for less than a kezayit.