A glottalic consonant is a consonant produced with some important contribution (a movement, a closure) of the glottis (the opening that leads from the nose and mouth cavities into the larynx and the lungs).
Glottalic sounds may involve motion of the larynx upward or downward, producing an egressive or ingressive glottalic airstream mechanism respectively. An egressive glottalic airstream produces ejective consonants, while an ingressive glottalic airstream produces implosive consonants. Ejectives are almost always voiceless stops (plosives) or affricates, while implosives are almost always voiced stops.
However, when a sound is said to be glottalized, this is not normally what is meant. Rather, glottalization implies that a normal pulmonic airstream is interrupted by closure of the glottis. Sonorants (including vowels) may be glottalized in this fashion. There are two ways this is represented in the IPA: (a) the same way as ejectives, with an apostrophe; or, (b) more properly with the under-tilde for creaky voice. For example, the Yapese word for sick with a glottalized m could be transcribed as either or . (In some typefaces, the apostrophe would occur above the em.) When an obstruent is glottalized but still uses a pulmonic airstream, it may be written ⟨ˀp⟩ etc.
When glottalic consonants of different types are present in a language, they tend to form a single phonological class. This can also be seen from how a language that has one kind of glottalized consonant is also more likely to have other kinds than could be expected by random chance. The connection is particularly strong between ejectives and glottalized sonorants, though this may be an areal feature rather than an inherent feature of the sounds in question. Furthermore, since none of the three types are very common, languages containing more than one type are still quite rare.
Read more about Glottalic Consonant: How To Produce An Implosive Consonant, How To Produce An Ejective Consonant, Distribution in The World's Languages