Imagine you are somewhere in the United States and you are TOTALLY lost -- for whatever reason, you have absolutely no clue where you are. You find a friendly local and ask, "Where am I?" He says, "You are 146 miles from Birmingham, Alabama."
This is a nice, hard fact, but it is not particularly useful by itself. You could be anywhere on a circle around Birmingham that has a radius of 146 miles, like this:
You ask somebody else where you are, and she says, "You are 246 miles from Charlotte, North Carolina." Now you're getting somewhere. If you combine this information with the Birmingham information, you have two circles that intersect. You now know that you must be at one of these two intersection points, if you are 146 miles from Birmingham and 246 miles from Charlotte.
If a third person tells you that you are 84 miles from Macon, Georgia, you can eliminate one of the possibilities, because the third circle will only intersect with one of these points. You now know exactly where you are -- Atlanta, Georgia.
This same concept works in three-dimensional space, but you're dealing with spheres instead of circles.