Social Engineering refers to any method of gaining illicit access to secured systems that relies not on technical skill, but rather on social and interpersonal skills for its success.
In practice, most social engineering "attacks" involve using misinformation, misdirection, or the everyday human rules of etiquette and reciprocity to cause people in positions of authority or responsibility to inadvertently make errors in judgement in which they provide access to key systems or key credentials incorrectly.
At one end of the spectrum, phishing is a kind of high-volume social engineering attack with which most contemporary users are familiar. In phishing, a malicious actor impersonates someone else in email, relying on brand recognition and authority to fool users into clicking on links to malware or to similarly false websites where they surrender their credentials happily. Phishing uses no special technical methods at all, but rather is simply a matter of fooling credulous users.
At the other end of the spectrum, individual impersonations by telephone are a classic form of social engineering in which a malicious actor calls a help desk or other privileged party within an organization, often claiming to have been referred by a colleague or to be an employee who has been locked out of their account. With the right manner, background knowledge, banter, and congeniality, the helpdesk worker or privileged party can often be fooled into granting access or providing secure credentials, which they imagine will help someone "on our team" to "get their work done." In fact, by providing these, they have enabled a malicious actor to enter a secured system without applying any particular computing techniques whatsoever.