* Starting in "The Emissary", we see a map of the galaxy showing territory explored. (The map is seen to the right of Worf in this image - http://tng.trekcore.com/gallery/albu...missary098.jpg
) The area covered seems more than the 19,000 light years (19% of the MWG) that Wesley said that the Federation had explored by then.
It is worth noting that the map is showing a two dimensional space, whereas (despite Star Trek's insistance that space is an ocean) the galaxy is three dimensional, and many star systems thick. So just because some area of space on that map was explored doesn't mean all of the represented volume was. There would be space above or below the explored portion that was unexplored, making explored space less than it appears on that map.