For the curious, a short, somewhat general description of how celestial navigation works is in order. Nathaniel, back me up here and correct any errors, I'm doing this without any reference materials.
Every star in the sky is at the zenith somewhere on Earth. Now, it might be daytime and you can't see that star, but it's still out there, straight up from a single point on earth. This spot is the ground point.
What if you could have a chart of a small collection of bright stars and their ground points at different times of the night and that chart would cover a year. Shazaam! That's exactly what we have with the
US Naval Observatory's Nautical Almanac.
So here's the way it's supposed to work. You see a star up there. The almanac tells you the ground point of that star. But it's not straight up for you. You take your sextant and measure the altitude above the horizon. There are complicated interpolations and correction factors we'll just pretend don't exist right now, pay no attention to the man behind the curtain.
Let's say the altitude of that star is 86º, That means that you are somewhere on a circle drawn around the ground point with the diameter of the linear distance described by that 4º difference from vertical. What good is a circle? We need more information.
So we pick another star, plot the ground point, measure the angle and draw the circle around THAT. Now we have two circles that intersect in probably two places. Errors can have bizarre consequences! Now we know we're at one of the two intersections, usually pretty good.
But a good plot is with at least three sightings. That way you get three circles that overlap in one spot. Plus you get more information! Those circles aren't going to intersect at a point, they will describe a triangle. Why? There are observational errors, possible computational errors. This triangle, by its size defines your error envelope. If you're in the US Navy, your error envelope better be smaller than a certain size or you're doing another set of observations!
So if your solution triangle is 100 miles on a side you have junk. If it's 1 mile on a side you did well!