This page forms part of an etymology course that gives an outline of the development of English. It is written in a sequence that you may want to follow. The best place to start, if you want to follow the whole course, is Etymology course, or, if you are only interested in English, Development of English. You may also arrive at any of these articles from other links. For more information about the history of English, you should of course read a good history of the language, such as Baugh (1993), Strang (1970), or Crystal (2005)
Present-day English is the term used by historians of language to describe the version of the English language that is current in this twenty-first century (and was current in the latter part of the twentieth century, too). It is the language in which I am writing, and you are reading, this text. A moment's thought will show you that the term present-day English includes innumerable different varieties of the language: all the local varieties spoken by those who have English as their first language (many in the UK, like cockney and East Hull, Edinburgh Morningside, Welsh valleys etc; as many in the USA, like southern Black Vernacular English, New England academic, Martha's Vineyard, Arkansas hillbilly etc; and national varieties throughout the world, like Indian sub-continental, Nigerian and Australian) and many spoken by those for whom English is not their mother-tongue, such as air pilots, business people and medics; varieties distinguished by their specialised use in professions, such as sailing, the theatre and construction; and the many different linguistic registers, such as formal academic, lovers' chat, and the language spoken in a pub.
So present-day English is not a single identifiable form of the language. It is a blanket term to describe any current version of the language. Thus it is a synchronous description, as opposed to the diachronous descriptions that are the usual subject-matter of etymology. Its usefulness lies largely, for newcomers to the history of language, in distinguishing what we now use from most of the previous versions that we may read in our studies.