What is it? Matzah that has come to contact with water either by cooking with water or dipping in water.
The Law: The Chassidic custom is not to eat any Matzah dipped in water due to a suspicion that part of the flour may not have been kneaded into the dough and thus now when it will come into contact with the water it will become Chametz. “Now although that this is not a complete and clear prohibition according to the letter of the law, nevertheless one who is stringent is blessed, and is not considered to be a wondrous person which does things without reason, as there is a great reason involved in order to avoid a suspicion of eating flour which was not kneaded into the dough and then came into contact with water, which is a Biblical prohibition according to many Rishonim.“…. “However one should not to protest against those that are lenient as they have upon whom to rely, mainly the Rambam and Rashi, although according to what the Arizal writes that one should be stringent on all the stringencies of Pesach, then it’s obvious that one should be stringent.”
On the last day of Pesach: On the last day of Pesach in the Diaspora one who is lenient to eat Matzah with water for the purpose of Yom Tov joy, is not losing out on keeping of the above mentioned stringencies of the Arizal. Our Holy Rabbeim were even scrupulous to dip their Matzas in liquids, and with each different food, in fish, meat, and especially soup. Even those foods which throughout the year are not normally eaten with bread, they would eat with their Matzah.
The Chabad custom: We are so stringent in the above that we make sure to place our Matzas in bags when we eat them, lest a crumb of it enter the food. Similarly, we check our cups and plates before we eat from them to make sure
Dipping Matzah in Fruit Juices: “Regarding dipping Matzah in fruit juice it’s obvious that one need/should not be stringent against doing it throughout the entire Pesach.” The Rebbe Rashab would eat his Matzas with wine [and milk]. If fruit juice is mixed with water then it is even more of a problem then plain water regarding its ability to ferment, being that plain water takes at least 18 minutes to ferment, while when mixed with fruit juice it can ferment immediately. Thus care must especially be taken that when eating Matzah with fruits etc, that there is no water around, including perspiration, on the fruit. Practically one may eat Matzah with avocado, tomato, oil. Nonetheless, despite the above, most Chassidim are accustomed not to eat Matzah with even fruit juice, perhaps due to worry of mixture of water or condensation.
Eating on vessels used with Gebrochts: The custom is to not use any vessels on Pesach which had wet Matzah fall on it that Pesach. However from a previous Pesach, it is not a problem to use even though no koshering was done.
May children eat Gebrochts on Pesach? In a letter from the earlier years the Rebbe writes that one may be lenient to with regards to children in feeding them Gebrochts. However in a Sicha of 1988 the Rebbe states that children should not eat Gebrochts on Pesach, being that Matzah is Emunah, and with faith one cannot be lenient. [However babies which will not be able to eat anything else, may eat Gebrochts, and it is better to eat it then to eat Kitniyos.]
May one take a bite off a large piece of Matzah or is one to only enter small pieces into his mouth? Some are accustomed to only enter bite pieces of Matzah into their mouth at a time, in order to prevent saliva [which is equivalent to water] from coming into contact with the bitten area. Rav Groner told me he never heard of such a custom.
Making/owning Gebrochts: The entire stringency of Gebrochts is only regarding eating it. It is however permitted to own Gebrochts. Accordingly, there is no problem with washing one’s floors that contain Matzah crumbs, even though one will come to bring them in contact with water, as one will not come to eat it.
 Shut Admur 6 [This letter is unique of its time, as it is the earliest known publication that deals with the prohibition of Matzah Shruya. The entire letter of Admur was dedicated to explain the basis behind the stringency.] See also: M”A 458/1; 459/16; Shaareiy Teshuvah 460/1 and 10;
Machatzis Hashekel 458/1; M”B 449/4; Piskeiy Teshuvos 458/5-8; Otzer Minhagei Chabad-Matzah Shruya; [A further detailed Halacha with footnotes/sources will be available online IY”H]