Glatt is the yiddish word for smooth. In Hebrew it’s chalak. In the Torah (Exodus 22;30) it says “You shall not eat meat from an animal torn (ie trefa) in the field”. Certain types of defects render an animal torn(trefa). The Shulchan Aruch (main codifer of Jewish law) lists the defects that make an animal a trefa. After an animal is shected (the term for the correct and complex way of killing an animal in Jewish law) they check the lungs to see if there is a puncture in them. If they see an adhension then it could possibly be kosher or possibly not. The Shulchan Aruch discusses these type of adhensions and most come out to be a problem and make the animal non-kosher (trefa) The Rema (Rav Moshe Isserlis, the commentary on the Shulchan Aruch which comments when Ashkenazic tradition differs from Sephardic [The Shulchan Aruch codifies the halacha with Sephardic tradion]) discusses different tests that can be done to lung adhensions to determine if they are kosher,accordingly making more animals kosher.
The Sephardim who follow the Shulchan Aruch eat only glatt meat that is termed glatt Beit Yosef. There is an Ashkenazic tradition that when there is very small adhensions (up to two) that can easily be removed it is rendered glatt according to Ashkenazim. Glatt meat is where the lungs are very smooth so there are very little adhensions. Beit Yosef glatt is even stricter then that as stated previously. When it says glatt it usually means the Ashkenazic defention of glatt. Glatt is a common stringecy that many people follow. That does not mean non-glatt is non-kosher. It is completely good for Ashkenazim (I’m not an expert on this so please speak to a Orthodox Rabbi on more about glatt, I’m just giving the general backround.)