To summarise means to re-formulate what someone else has written (said, etc.) in abbreviated form. Whereas a paraphrase may be of equal length to the source text, a summary is considerably shorter.
Just as in quotations and paraphrases, summaries require a reference to the source.
A note on spelling: 'summarise' can also be spelled 'summarize'. In British English, both forms are accepted and in American English, the form 'summarize' is used.
When to summarise
Summaries are made when there is a need to condense large units of texts or other forms of data. In summarising, the main ideas of the whole text (or a large part of it) are thus reformulated and condensed.
Students may be asked to summarise a course book or article, and scholarly articles may include summaries of previous research in order to introduce the new research that is being presented.
Although summarising is a good way of presenting in brief the contents of a certain text, theory, interview, etc., it is important to note that in a pure summary, the writer may only summarise a source, not present any new data or ideas.
Summarising is used to briefly represent what previous books, articles, etc. have expressed. Unless specifically stated in a course assignment, for instance, an academic essay can therefore not merely consist of summaries of previous studies.
Summarise or paraphrase?
For the distinction between summary and paraphrase, see the AWELU section on paraphrasing: