So if you can get above the thickest part of the atmosphere, say attached to a giant goofy-looking airplane, before you light off your engine - rather than having to push your way through that same thick air on your own - you need less propellant, overall, to reach orbit, which means you can devote a larger fraction of your launch vehicle's mass to payload.
Space shuttle was 3 g - 1 from gravity = 2g net acceleration, but that's kept low for passengers. Even then 2 g net ~= + 44 MPH every second.
So, first 15 seconds your going under 660 MPH which is not that fast, but you get ~1.4 miles up. Because drag increases with speed very quickly the next bit is harder, but you very quickly get above what an aircraft could take you with ~5.6 miles at 30 seconds. Note: Higher g's mean more drag in denser atmosphere, but less gravity drag it's a meaningful trade-off.
However, aircraft's velocity is very useful essentially saving those first 15 seconds of full burn, but comes at the price of needing more structural elements to support the hanging rocket.