Modal Verbs are used to express ideas such as ability, necessity, permission, and possibility.
There are not many modal verbs: can, could, dare*, need*, may, might, must, shall, should, will, would. There are also modal constructions: be able to, ought to, be allowed to.
For more, see Modal Verbs.
In grammar a Verb Tense is a form of a verb used to indicate roughly the time when the action described by the verb takes place. Here we talk about 3 basic tenses: Past, Present and Future. (Some people talk about more than 3, however.)
Compare this with Verb Form which is the form of a verb in a particular tense, e.g. present simple, present continuous, etc.
For more, see Verb Tenses & Forms in English Grammar.
Vocabulary is the number of words you know. Learners have an Active Vocabulary which are the words they use when they speak or write; they also have a Passive Vocabulary which are the words they may well understand but do not actively use.
For more, see Vocabulary and TEFL.
Pronunciation is simply the way in which words and phrases are spoken.
For more, see Pronunciation in English.
Students learning English are often described as Beginners, Intermediate or Advanced. Roughly speaking this is their level, i.e. how much English they know, how well they can speak and understand and so on.
For more, see Learner Levels in TEFL.
Verbs tell us about an action; they are sometimes called doing words or action words. Verbs describe what is happening:
run, walk, read, talk
For more, see Verbs in English Grammar,
Parts of Speech (often abbreviated to PoS and sometimes known as Word Classes) are the different categories of words in English. They refer to the way in which those words are used grammatically.
Common PoS include adjectives, nouns, verbs, adverbs and so on.
For more on this, see Parts of Speech in English Grammar.
An Idiom is a phrase which has a figurative meaning which is very different from the literal meaning. For example, in The Godfather famously Luca Brassi sleeps with the fishes which does not literally mean that he sleeps with undersea creatures but that he is dead.
For more, see Teaching Idioms in TEFL.
EAP or English for Academic Purposes is usually concerned with teaching English to students who are involved in higher education at an English speaking university or college.
For more, see EAP - English for Academic Purposes.
Business English is English as it is used in the business workplace. It focuses on business phrases and typical workplace vocabulary often used for negotiations, telephone conversations, interviews, presentations, meetings, etc.
For more, see Business English.
Beginners are starting out learning English. The might know nothing at in English or they might be able to say a few phrases, give their name and have very simple conversations.
Read more: Beginner Level Students in English.
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.