well, a simpler example among many will be water level, on the surface of a body of water, namely lake or ocean or else, we(humans) count anything above the water as a positive integer, and anything below the water a negative one, so say a Pelican flying at 30 meters above water is +30m above, and then dives down to say 20 meters to get a fish, namely the Pelican has dived to a depth of -20m, it went from +30m to -20m, and then flies back up with its fish say 50m, so is +50m.
negative integers are always dependent on a point of reference, in the example before, the point of reference was the water level, but could be many things.