Not all adverbs end in -ly, but many do.
Like all adverbs, -ly adverbs are used to add meaning to verbs, adjectives, and other adverbs. For example:
Jones deals honestly with all his customers. (adverb modifying the verb deals)
The lecture on adiabatic and isochoric kinetics was mercifully brief. (adverb modifying the adjective brief)
The concert is over. You have arrived unfortunately late. (adverb modifying the adverb late)
Some -ly adverbs can also be used to modify an entire sentence. For example:
Honestly, most television comedies are unbearably vulgar. (adverb modifying entire sentence)
Mercifully, the blast was prevented by the swift arrival of the fire brigade. (adverb modifying entire sentence)
Fortunately, the ship stayed afloat long enough for all the passengers to be rescued. (adverb modifying entire sentence)
In each of these examples, the adverb at the beginning of the sentence is set off by a comma and conveys the attitude of the speaker toward the entire thought being expressed.
Generally speaking (as opposed to more precise classifications in linguistics) adverbs used in this way are called “sentence adverbs.” Here is a list of other adverbs that may be used as sentence adverbs:
Note: Some last-ditch language sticklers reject the right of hopefully to be included in this list. According to these cranky holdouts, the only meaning for hopefully that “careful writers” should recognize is “with hope,” as in “My dog Cash stared hopefully at the treat jar.” They reject the notion that hopefully can also be used to introduce a sentence with the sense of “I hope” or “it is to be hoped,” as in this sentence: “Hopefully, the new millage will pass, and we can expand the library.”
English speakers have been using hopefully as a sentence adverb for eighty years at least—possibly longer. “Careful writers” may continue to avoid its use as they wish, but ridiculing its use by others is bad form.