Abugida is a term coined by Peter T. Daniels for a script whose basic signs denote consonants with an inherent vowel and where consistent modifications of the basic sign indicate other following vowels than the inherent one.
Thus, in an abugida there is no sign for "k", but instead one for "ka" (if "a" is the inherent vowel), and "ke" is written by modifying the "ka" sign in a way that is consistent with how one would modify "la" to get "le". In many abugidas the modification is the addition of a vowel sign, but other possibilities are imaginable (and used), such as rotation of the basic sign, addition of diacritical marks, and so on.
The obvious contrast is with syllabaries, which have one distinct symbol per possible syllable, and the signs for each syllable have no systematic graphic similarity.
The name is derived from the first four characters of an order of the Ethiopic script used in some religious contexts (this order seems to correspond to the ancestral semitic character order (aleph, beth, gimel, daleth / ABCD / ...). The Ethiopic script is an abugida, although the vowel modifications in Ethiopic are not entirely systematic. Many North American Indian scripts, such as Cree syllabary, are abugidas as well. The largest single group of abugidas is the Brahmic family of scripts, however, which includes nearly all the scripts used in India and Southeast Asia.