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.

Oxford English Dictionarysummarize, verb. To make (or constitute) a summary of; to sum up; to state briefly or succinctly. summary, noun. A summary account or statement [where the adjective "summary" is defined in the following way by the OED: "Containing or comprising the chief points or the sum and substance of a matter; compendious (now usually with implication of brevity)"].

When to summarise

Summaries are usefulwhen 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 thus 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.

Should I summarise or paraphrase?

For the distinction between summary and paraphrase, see the AWELU section on paraphrasing:

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