I understood what it is from the following link:
http://electronics.howstuffworks.com/gadgets/travel/gps1.htm
But I want to know :
In a 2D plane, if we know the (x, y) positions of three “guard” points a, b, c and the distances of a point p to a, b, c – say da, db, dc – how to know the (x, y) position of point p
Given a,b,c, and da,db,dc . How to find the point p?
Geometrically speaking, it is straightforward: just draw the two circles with midpoints $a,\ b$, and lengths $d_a$ and $d_b$. Unless things go wrong, these two circles intersect in two points $p_1,p_2$. Now, just compare distances from $p_i$ to $c$ - again, exactly one should be $d_c$.
Analytically speaking, you can write out coordinates of your points $a = (x_a,y_a)$, etc. The conditions about distances translate into $d_a^2 = (x_a - x_p)^2 + (y_a - y_p)^2$, etc. These are three equations in two unknowns, so assuming they have a solution, it is almost certainly unique. Note that subtracting the equation for, say, $a$, from the remaining two equations you make them linear, and thus easy to solve in principle (the exact formula won't enlighten you much, I believe).
Note that much of the given data is redundant: given $d_a,\ d_b$, there are generally just $2$ values of $d_c$ that make sense!