Pragmatics studies the factors that decide our choice of language in social interaction. It looks at the social rules that affect our choice.
It looks at the meaning of speech acts and the intention of the speaker and includes information about the social status of the speakers, cultural features such as politeness and formality, and both explicit and implicit linguistic features.
Focus and content:
Pragmatics overlaps at times with semantics, stylistics, sociolinguistics, psycholinguistics and discourse analysis.

Aspects:
Some of the aspects of language studied in pragmatics include:
(taken from Shaozhong Liu’s pragmatics page.)

Deixis: meaning 'pointing to' something. In verbal communication however, deixis in its narrow sense refers to the contextual meaning of pronouns, and in its broad sense, what the speaker means by a particular utterance in a given speech context.
Presupposition: referring to the logical meaning of a sentence or meanings logically associated with or entailed by a sentence.
Performative: implying that by each utterance a speaker not only says something but also does certain things: giving information, stating a fact or hinting an attitude. The study of performatives led to the hypothesis of Speech Act Theory that holds that a speech event embodies three acts: a locutionary act, an illocutionary act and a perlocutionary act (Austin, 1962; Searle, 1969).
Implicature: referring to an indirect or implicit meaning of an utterance derived from context that is not present from its conventional use.
Pragmaticians also explore why speakers can successfully converse with one another in a conversation.
A basic idea is that interlocutors obey certain principles in their participation so as to sustain the conversation. One such principle is the Cooperative Principle which assumes that interactants cooperate in the conversation by contributing to the ongoing speech event (Grice, 1975).
Another assumption is the Politeness Principle (Leech, 1983) that maintains interlocutors behave politely to one another, since people respect each other's face (Brown & Levinson 1978).
A cognitive explanation to social interactive speech events was provided by Sperber and Wilson (1986) who hold that in verbal communication people try to be relevant to what they intend to say and to whom an utterance is intended.
The pragmatic principles people abide by in one language are often different in another. Thus there has been a growing interest in how people in different languages observe a certain pragmatic principle. Cross-linguistic and cross-cultural studies reported what is considered polite in one language is sometimes not polite in another.
Criticisms
A traditional criticism has been that pragmatics does not have a clear-cut focus.
Other complaints are that, unlike grammar which resorts to rules, the vague and fuzzy principles in pragmatics are not adequate in telling people what to choose in face of a range of possible meanings for one single utterance in context.

However, there is a consensus view that pragmatics as a separate study is necessary because it handles those meanings that semantics overlooks (Leech, 1983)
The study of speech acts, for instance, provides explanations of sociolinguistic conduct. The findings of the cooperative principle and politeness principle also provided insights into person-to-person interactions.
Deixis, for instance, is important in the teaching of reading. Speech acts are often helpful for improving translation and writing.