English for Specific Purposes (also sometimes called English for Special Purposes) refers to a situation where a learner has a particular need for the language, and follows a course which aims to meet that need without including any language which is irrelevant to it. The two most common fields within ESP are English for Occupational Purposes (where the learner has work related needs), and English for Academic Purposes (where the learner is studying in order to eg complete a university course in English, to write academic papers for publication etc). However, any learner with a well-defined need could potentially come under the ESP umbrella - for example a learner with a specific hobby (gardening, football etc) which s/he wanted to be able to read about and chat about in internet discussion groups in English.
ESP courses would generally start with a needs analysis which would define what the learner has to do using English - the situations in which they will need to communicate (eg business meetings, international conferences, university lectures, internet forums), their interlocutors and role relationships (eg client-salesman, teacher-student, nurse-patient, peer-peer), the tasks they will have to carry out (eg writing an academic essay, negotiating contracts, answering forum posts), and the language needed for those tasks in terms of topic related lexis, functions and structures etc. The course is then designed to cover these areas.