As a bound morpheme, it generally indicates that the word to which it is bound is an adverb, formed from an adjective by the rule add -ly to make an adjective into an adverb. For example, "elegantly" (adj) formed from "elegant" (adv), etc.
However, there are adjectives ending in -ly that are adjectives, and not all adverbs end in -ly, notably most bare adverbs. A small minority of bare adverbs end in -ly, e.g. ugly (the adverb form of which can be uglily or ugly).
Another bound morpheme may be bound after -ly, in which case the spelling changes from -ly to -li-, e.g. manly --> manliness.
In addition, there are a number of nouns and verbs that are spelt ending in -ly, and most (though not all) of these don't contain the -ly morpheme. For example nouns; ally, butterfly, gully, jelly, jolly, lily, orderly, supply. And verbs ally, apply, bully, imply, multiply, rely, supply, sully, tally, etc.
-ly is a cognate with Dutch "-lijk", German "-lich" Swedish "-lig", and a doublet with the suffix -like. Many English adverbs ending in -ly have the same root as French adverbs that end in -ment, e.g. rarely/rarement.