Short answer
The greek word translated as "babbler" in Acts 17:18 is a piece of Athenian slang, meaning: "an empty speaker, an ignorant, a vulgar plagiarist", commonly used to define those bad preachers of the rabble, from the street-corners of the market place.
For Paul as a man, it's an insulting word. For Paul as a preacher, it's a diminishing word.
Long answer
You need to look at the original word if you want to have an accurate definition, especially in historical books, like Acts, where you need to check the historical context in which the word is applied.
The word itself in the original Greek language is spermologos (σπερμολόγος Strongs nt 4691). In Thayer's Greek Lexicon we read (emphasis mine)
[...] hence, beggarly, abject, vile (a parasite); getting a living by
flattery and buffoonery, Athen. 3, p. 85 f.; Plutarch, mor., p. 456
d.; a substantive, ὁ σπερμολόγος, an empty talker, babbler
(Demosthenes, p. 269, 19; Athen. 8, p. 344 c.): Acts 17:18
So we can see that the word, in this context, has the meaning of "an empty speaker", which is a pejorative label for a preacher or a public speaker. But further researching has led me to Abraham J. Malherbe's Light from the Gentiles: Hellenistic Philosophy and Early Christianity, p. 213, where we read:
The first question, using the pejorative σπερμολόγος, effectively
ranks him [Paul] with the no-good street preachers of the day as described by
Dio Chrysostom: they post "themselves at street-corners, in alleyways,
and at temple-gates, pass around the hat, and play upon the credulity
of lads and sailors and crowds of that sort, stringing toguether rough
jokes and much babbling [σπερμολόγος] and that rubbish of the
marketplace." (Dio Chrysostom, Or. 32.9)"
With this reference, it becomes clear that σπερμολόγος is being used in a very pejorative way, meaning "an empty speaker" and equating Paul with bad street preachers of the time.
We also have a good definition of this term in Parsons-Culy's Acts: A Handbook on the Greek Text
σπερμολόγος. According to Louw and Nida, this term may refer either to (1) a person "who acquires bits and pieces of relatively
extraneous information and proceeds to pass them on with pretense and
show" (thus, "ignorant show-off, charlatan"), or (2) a person "who is
not able to say anything worthwhile in view of his miscelaneous
collection of tidbits of information" (thus, "foolish babbler").
Barret suggets that the expression refers to a person who has stolen
ideas from other and used them as his own.
Conclusion
After all the research, I can agree with R. J. Knowling, from Expositor's Greek Testament, when he mentions a Sir W. M. Ramsay's article, where is written that
"there is no instance of the classical use of the word as a babbler or
mere talker, and [that] he sees in the word [σπερμολόγος] a piece of
Athenian slang, [...] applied to one who was quite outside any
literary circle, an ignorant, vulgar plagiarist".
