(adjective)- Loosely now, painterly is a descriptive word meaning "this has the attributes of painting." What's that? Not clear enough? Try this, then: "Shapes in a painterly composition aren't sharply defined and the whole piece may be showing obvious brushwork."
The easiest way to get a bead on painterly is to visualize it as the opposite of linear. Think of any van Gogh you've seen. It's full of areas of color that blend into one another, and Vincent clearly didn't care if his brushwork was showing. It's up to your eye to fill in the blanks and define shapes. That's "painterly." A linear composition, on the other hand, does all of that work for you. Think here of a coloring book, which is about as linear as things can get.
Since this is an Art History site, we'll stick to painterly paintings - although it's worth noting that this adjective is used to preface other nouns such as "prose" and "effect." Additionally (I warn you) every single person who has painted, paints or will paint in the future has his or her own parameters for that which constitutes "painterly." Smile if you will, but more than one heated debate has arisen over personal opinions on the subject.