Federation Standard (or just Standard) is the most prevalent and most used language in the galaxy. Based off of a mix of early human languages and Linguacode, its popularity with members of the Federation spread. It was symbolic of the unity of the United Federation of Planets to have a unified language. Though similar to the English language of Earth, it is not entirely the same (see below).
Most sentient species that make galactic contact can and do speak Standard in addition to whatever native or regional language they might use on a daily basis. Some beings normally do not possess the organs necessary to speak Standard. Whether or not a being can speak Standard, it is usually in their best interest to comprehend it, and most do.
Behind the scenes
In the television shows, films and books, Standard is the same as English. In translations to non-English languages, Standard is assumed to be reciprocally the same language as the one being used. As a result, spoken Standard is considered dubbed and written Standard text is considered translated.