Academic language is the term used here for the grammatical and lexical features of academic writing. Academic writing is the writing done for and by academics, i.e. the teachers and researchers in academic institutions such as schools and universities.
There are two distinct features of academic language: grammatical and lexical.
Grammatical feature: sentence complexity
One typical grammatical feature of academic language is sentence complexity. Everyday spoken and online communication typically consists of short simple sentences. In contrast, in academic language the sentences are much longer and often contain several clauses.
Here is an example of two consecutive complex sentences from a Wikipedia article on pragmatics:
Unlike semantics, which examines meaning that is conventional or "coded" in a given language, pragmatics studies how the transmission of meaning depends not only on structural and linguistic knowledge (grammar, lexicon, etc.) of the speaker and listener but also on the context of the utterance, any pre-existing knowledge about those involved, the inferred intent of the speaker, and other factors. In that respect, pragmatics explains how language users are able to overcome apparent ambiguity since meaning relies on the manner, place, time, etc. of an utterance.
In such academic language it is common to start sentences with a dependent clause, such that the main subject of the sentence is delayed. The subject of the first sentence in the quote above is shown in bold.
Grammatical feature: Heavy noun phrases
A second typical grammatical feature of academic language is heavy noun phrases. These may result from the desire to pack a lot of information into a singular grammatical constituent and thereby avoid the need to expand the text with a clause or a prepositional phrase.
For example, the rejected school council cafeteria extension proposal, which when expanded would need to read something like the proposal by the school council to extend the cafeteria which was rejected.
The 38 first words of this sentence constitute a heavy noun phrase before the appearance of the verb have filled:
Videos showing the outpouring of anger among the protesters both in the USA and around the world over images of the violent death of George Floyd which they see as a evidence of systemic racism and police brutality have filled the news.
Grammatical feature: Nominalization
A third grammatical feature is nominalization. So, for example, You should consider... becomes Consideration should be given to... . And We expect that... becomes The expectation is that... .
Nominalization often results in less readable text. Compare, for example, Monkeys fight about toys, just like children with Fights about toys are equally common among monkeys as among children.
The passive is common in academic text. This is because it is a good way to remove the agent, who is either unknown or clear to the reader and therefore unnecessary. Constructions such as the following proliferate: It is expected that... (instead of We expect that.... And Ticks are classified as arachnids (instead of Zoologists classify ticks as arachnids).
The passive is also useful because it allows the writer to place the most important information at the start of the sentence and make it the subject. Compare Two pathologists carried out the investigations into the sudden death of the patients with The investigations into the sudden death of the patients were carried out by two pathologists (passive).
It is clear that academic text is full of the vocabulary of that discipline. Zoology texts, for example, will be full of words such as physiology, taxonomy, heredity.
But there is also a general academic vocabulary that contains words which are prevalent in all academic disciplines. This site has a list of the most common academic words, including short academic extracts in which the words are exemplified.
Some examples are hence, conversely, correspond, whereas, fluctuate, subsequent, trace, vary, evident, principle, regulate, scarce.
It is important that students learn how to write academically since being able to do so is necessary to success in examinations. It is also very important that they learn the general academic vocabulary that is the basis of academic text.
A further strong recommendation is that students read the kinds of texts that the aspire to produce themselves. In this way they can also learn the academic conventions in that particular discipline, including text structuring.
Here is an external webpage that discusses some of the academic writing conventions and has further examples of what and what not to include in Academic Writing.
Here is another page discussing the features of academic writing.