This is opposed to synthetic languages, which synthesize many concepts into a single word, using affixes regularly.
Typically, analytic languages have a low morpheme-per-word ratio, especially with respect to inflectional morphemes.
The most prominent and widely used Indo-European analytic language is Modern English, which has lost much of the inflectional morphology that it inherited from Proto-Indo-European, Proto-Germanic and Old English over the centuries and has not gained any new inflectional morphemes in the meantime, which makes it more analytic than most other Indo-European languages.
For example, Proto-Indo-European had much more complex grammatical conjugation, grammatical genders, dual number and inflections for eight or nine cases in its nouns, pronouns, adjectives, numerals, participles, postpositions and determiners, Standard English has lost nearly all of them (except for three modified cases for pronouns) along with genders and dual number and simplified its conjugation.
A related concept is that of isolating languages, which are those with a low morpheme-per-word ratio (taking into account derivational morphemes as well).