What is "Matzah Ashira"?

That's matza which is not just flour and water, but instead of water- they use eggs, oil or fruit juice. This is not kosher for the mitzva of matza at night, and ashkenazim say it's forbidden to eat all Pesach (they feel that it may ferment) but even they allow to keep in one's home. Regarding Sefaradim- some allow it on Pesach while others forbid it (some cookies also are called "Matza Ashira", meaning they are allowed for those Sefaradim who eat Matza Ashira, when it's allowed for them, e.g. the day before Pesach until about 4 pm, and for those who eat it all Pesach). It's generally used on the Shabbat before Pesach for people who want their homes already Kosher for Pesach, but need to fulfill the Shabbat meals without bread and without matza (for it's forbidden to eat matza on the day before Pesach, and many have the custom not to eat matza already 2 or even 4 weeks beforehand). It's also allowed for elderly people for the week of Pesach (but not for the matza at the Seder!), who have difficulty digesting matza.