Phonology is a branch of linguistics concerned with the systematic organization of sounds in languages. It has traditionally focused largely on the study of the systems of phonemes in particular languages (and therefore used to be also called phonemics, or phonematics), but it may also cover any linguistic analysis either at a level beneath the word (including syllable, onset and rime, articulatory gestures, articulatory features, mora, etc.) or at all levels of language where sound is considered to be structured for conveying linguistic meaning. Phonology also includes the study of equivalent organizational systems in sign languages. 

The word phonology (as in the phonology of English) can also refer to the phonological system (sound system) of a given language. This is one of the fundamental systems which a language is considered to comprise, like its syntax and its vocabulary. 

Phonology is often distinguished from phonetics. While phonetics concerns the physical production, acoustic transmission and perception of the sounds of speech, phonology describes the way sounds function within a given language or across languages to encode meaning. For many linguists, phonetics belongs to descriptive linguistics, and phonology to theoretical linguistics, although establishing the phonological system of a language is necessarily an application of theoretical principles to analysis of phonetic evidence. Note that this distinction was not always made, particularly before the development of the modern concept of the phoneme in the mid 20th century. Some subfields of modern phonology have a crossover with phonetics in descriptive disciplines such as psycholinguistics and speech perception, resulting in specific areas like articulatory phonology or laboratory phonology.
And the other name?
(and therefore used to be also called phonemics, or phonematics),