19% of the galaxy is ridiculously large and it's completely unrealistic that is has been explored by the federation. Mapped by telescopes and drones maybe but not explored, just for reference 19% of the galaxy would be 19 BILLION stars by the most conservative estimates of the number of stars in our galaxy and it's likely to be way more.They don't mention a percentage in "Encounter at Farpoint" or "All Good Things". They do mention a percentage in "The Dauphin", a second season episode. Wesley has a crush on a teenage girl who's soon to be ruler of a world, then takes her out to the holodeck, and tells her the Federation has only explored 19% of the galaxy.
The federation was around 200 years old at that point but lets be generous and give them 350 years of exploration by including what the members did before joining the federation. If they had visited 100 new stars systems per day that would put them at 12.8 million stars or 0.0128% of the galaxy and that's just visiting once with no exploration of the star system itself or any stuff in between the stars like giant space amoeba, various nebulas, relics from ancient civilizations etc.
Let's go nuts and assume the federation managed to visit 10.000 stars per day for 350 years, that's a completely unrealistic number but if they managed to do it that still would only give them 1.28% of the galaxy explored and like I said above those number are only true if we assume 100 billion stars in the galaxy, it could be up to 400 billion.
So to answer what's left to explore, pretty much everything, the federation has barely scratched the surface of the galaxy.