A fellow in its broadest sense is someone who is an equal or a comrade. When describing the term in relation to colleges the term refers to an incorporated (not in its legal sense) member of such a body of people.
As a consequence, in the language of British academia, a fellow is a scholar who is financially supported by a college or university, for the purposes of research and/or teaching.
However, not all such people actually hold the title of "fellow", and it is difficult to establish precise rules for application of the title. In the newer universities, research fellowships are nearly always temporary posts, awarded to people who have completed doctoral and postdoctoral studies. (Persons of lesser seniority are usually called research assistants, and academics with permanent salaries are more often called lecturers.)
In the older British universities many fellows have pastoral responsibilities for the students of their own colleges.
At Cambridge University fellows are among the most senior of the academic staff at the college, and are not only responsible for teaching, research and the pastoral care of the students; they also form a council to support the Master (or equivalent - e.g. Principal at Homerton College ).
The term may also be used to define a level of membership within an organisation for example to say that one is a Fellow of the Royal Society. Fellows are usually the highest ranking members of the organisation, outranking members, licenciates , and affiliates.
Historically the word fellow was used to describe a man, particularly by those in the upper social classes.