GPS works because there are a number of very accurate clocks in satellites. The satellites broadcast the current time on radio frequencies. That travels out at the speed of light. Since the speed of light is very fast, but not instant it takes some amount of time for the time info to reach the gps receiver (thing in your hand that tells you where you are). The receiver can then figure out how long the signal took to reach it from the satellite. Since the speed of light is known the receiver then knows how far away the satellite is. The location of the satellite above the Earth is also known. Knowing all these things allows the receiver to figure out it must be on a sphere whose center is the satellite.
To think about this, if I told you I was 100 miles from New York City, you would be able to draw a sphere whose surface I must be on. At first you may think a circle, since we are used to dealing with flat surfaces, but remember I could be 100 miles directly above NYC, that's why it's a sphere.
So one satellite gets you a sphere, and if you add another one it adds a different sphere. You must be somewhere where these two spheres touch, since you must be on the surface of both. Going back to cities, if I told you I was also 300 miles from Philadelphia you could draw a second circle. There would be only two points where both circles touched, and I would have to be at one of those. Again really it would be two spheres, as I could be in the air. If you keep adding satellites it keeps limiting the spots you could be. When you have 4 satellites you have enough to know there is only 1 spot you could possibly be.
To review the atomic clock is just a very accurate clock, which is needed because you are measuring tiny fractions of a second. The satellite just broadcast the time, and their location. The receiver only receives, it doesn't send anything back to the satellites.