Informally, an ology is a field of study or academic discipline ending in the suffix-ology.
Etymology
The word ology is a back-formation from the names of these disciplines. "-logy" basically means "the study of _____". Such words are formed from Greek or Latin roots with the terminal -logy derived from the Greek suffix -λογια (-logia), speaking, from λεγειν (legein), to speak. The word ology is thus misleading as the 'o' is actually part of the word stem that receives the -logy ending. For example, the bio part of biology stems from Greek βιος (bios), life. This is why some of the words do not end in -ology (such as mineralogy).
Other words ending in "ology"
Not all words ending in -ology are ologies in the above sense. In some words such as tautology and haplology, the -logy suffix is from the Greek λογος, word, and denotes not a field of study but a type of speech or writing. For example, haplology means the mistake of saying one letter, syllable or word when two or more are required, as in the example of pronouncing the word February somewhat like "Febuary".
It should also be pointed out that some words mean to study something, but aren't called ologies – midwifery is one example.
Usage
Although technically incorrect, "-ology" is sometimes used to describe a subject rather than the study of it. Technology is a typical example. This usage is also widespread in medicine; for example, pathology is often used for specific disease ("We have not found the pathology yet").
"Ology" can be appended to any word, humorously, when describing its study; such as beer-ology or Wiki-ology.
The ending "ologist" is used to describe a person, so biology gives biologist, and so on.
A famous Britishtelevision commercial of the 1980s has a Jewish student calling his grandmother (played by Maureen Lipman) to confirm his exam results. He is disappointed that he has only passed Sociology, but his grandmother will have none of it. "Anthony," she insists, "if you get an ology, you're a scientist!"
Archaeozoology, the study of relationships between humans and animals over time through examination of animal remains at archaeological sites (also see Zooarchaeology)
Genealogy (commonly misspelt and mispronounced as "geneology"), the study of relationships within families particularly with a view to constructing family trees
Genecology , the study of genetic differences in relation to the environment
Odontology , the study of the structure, development, and abnormalities of the teeth
Omphalology, facetious name for the non-existent medical specialty that treats of navels, which has been used in a manner similar to the way the word widget is used in economics textbooks
Phenomenology, the study and science of phenomena as distinct from the science of actual existence or being; also a movement founded by Husserl which studies conscious experience without its metaphysical concerns
Zooarchaeology, the study and analysis of animal remains at archaeological sites to reconstruct relationships between people, animals, and their environment (also see Archaeozoology)
Eulogy, though not an -ology, is a commemoration of a person's life at his/her funeral.
Hagiology is literature dealing with the life of a saint or, indeed, any revered person, a biography of an individual, rather than a study of saints, sainthood or saintliness in general.
Philology, the historical study of languages. This is not a ology in the strict sense, because it is not the study (-ologia) of love (philo-), but the love (philo-) of literature (logia).
Phraseology is the way words are put together, therefore the style being used in a sentence, or the set of phrases or the choice of words used by any particular group of people, a type of register, then, that reflects the form of language used in a certain social situation in which particular subjects are being discussed. Examples of register (phraseology) are: (obscene) slang, legal language (legalese), journalese, the jargon of the racecourse, or the special words or phrases used in certain occupations, as only a few of a very numerous category.
Piphilology seems to be a borderline case with some aspects of a field of study, but not a scientific discipline.
Reflexology, alternative method of massage, therapy or pressure on certain points of the sole of the feet as a means of relieving nervous tension.
Scientology, the belief system/cult religion founded by L. Ron Hubbard, self-described as a study of knowledge.
Terminology, a set of words and/or phrases, usually in relation to some particular canon or field of study e.g. 'mathematical terminology'.
Tetralogy of Fallot, an abnormality of the heart consisting of four deformities that often occur together.
Trilogy (although not strictly an -ology) is a body of writing in three parts, as tetralogy is that in four parts. Other words such as pentalogy, hexalogy, and heptalogy or septology cover larger series.
Tropology , the use of tropes in speech or writing.