The name for this particular practice has come to stand for more stringent kashrut standards in general.
There are many distinctions among subgroups of traditionalist Jews. Even among those labeled Orthodox, a distinction is sometimes drawn between common standards of kashrut and the more stringent standards that some adopt. The latter, known generally as "la-mehadrin"(for the ritually particular) or just "mehadrin," is often mistakenly labeled as "glatt kosher."
In this article, an expert in Jewish law explains just what "glatt kosher" really means. Rabbi Zivotofsky's monthly series of columns entitled "What's the Truth About...?" is "devoted to researching commonly-held beliefs." The body of the article is reprinted in full, but additional bibliographic material in the notes may be found in the original article. The terms "animal" and "meat" are used here somewhat idiosyncratically, to refer to kosher mammals and their flesh but not to fowl and the flesh of fowl. The author and publisher note that "this material is for study purposes only and should not be relied upon for practical halakhah. One should consult his own competent halakhic authority for specific questions."
Reprinted from Jewish Action 60:2, Winter 1999, published by the Union of Orthodox Jewish Congregations of America
"Glatt Kosher" means something like "extra kosher" and applies to chicken and fish as well as meat.
Glatt is Yiddish for smooth, and in the context of kashrut it means that the lungs of the animal were smooth, without any adhesions that could potentially prohibit the animal as a trefa, an issue only applicable to animals, not fowl or nonmeat products.
In colloquial discourse, tref refers to anything that is not kosher. The technical definition of trefa is based on Exodus 22:30 ("Do not eat meat from an animal torn [trefa] in the field") and refers to an animal with any of a specific group of physical defects that are detailed in the [Babylonian] Talmud (most of the third chapter of Hullin; 42a-59a) and [traditional Jewish law] codes (Maimonides, Mishneh Torah, Laws of Forbidden Foods 4:6-9 and Laws of Slaughter ch. 5 -11; Shulchan Arukh, Yoreh De'ah ["YD"] 29-60). Examples of these "defects," which often go far beyond the health inspection of the USDA, include certain lesions, lacerations, broken limbs, missing or punctured organs, or the result of an attack by a larger animal. Such defects can occur in, and thereby render, both animals and fowl tref. Because most of these defects are uncommon, it may be assumed that most animals are healthy (Shach [commentary to Shulchan Arukh], YD 39:1) and hence there is no requirement to inspect every animal for them. (This does not imply that a blind eye may be turned to their presence.)