Defining a student as intermediate is a very approximate classification of how well they speak English. There is no set definition of what intermediate means, however as a very rough guide students at intermediate level can talk and read about a wide number of subjects using appropriate vocabulary and fairly correct, if basic, grammar. They can confidently use all the main tenses, and are beginning to use phrasal verbs, modal verbs, and suchlike.
Tone and style are not refined yet but there is an awareness of pronunciation and what it entails.
An intermediate level student has generally enough knowledge of the language to branch out to more specific English courses, such as Business English or English for Academic Purposes.
A Pre-Intermediate level gives scope for improvement in all areas (grammar, vocabulary, pronunciation, etc.) as students have a good basic ability to communicate and understand. They can confidently use all the simple tenses and handle many everyday situations like shopping, booking a hotel room, asking for information, etc. Grammatically they have generally covered the main parts of speech and know how to use them.
At Upper-Intermediate level students have an effective, but not perfect, use of English. They can take part in extended conversations on a wide range of topics. If they don't know the appropriate term for something they are able to find a way of describing it. They have a knowledge of some idiomatic English and colloquial expressions. All main areas of English grammar have been covered at this level.