What this emblem means to Masons.
The square is a builders square, two equal flat-edged metal or wooden arms joined at a perfect right angle (90 degrees), used to measure and confirm perfect square corners for drawings, carved stones, and buildings. The right angle is important in buildings, to make sure that stones, bricks, walls meet and rise at the correct angle, so they dont crowd each other, or lean improperly. To Masons, the square symbolizes virtue and honesty with one another, as in the saying "a square deal" which of course means an agreement that is fair to both sides. It also symbolizes the authority of the master of the workmen, against whose perfect square all the other measuring squares on the building site are checked for accuracy. In early days, the simple techniques for the geometric construction of a perfect square were secrets held by master builders, so the master (presiding officer) of a Masons lodge still wears a square as his emblem.
The compasses are a pair of legs of equal length, fixed to each other at one end by an adjustable hinge. They are used for drawing circles, where one point of the compasses is the fixed center and the other swings around to trace the circumference. The compasses can also be used for taking or marking off distances along a line. To Masons, the compasses symbolize learning to draw a circle around our own desires and passions, learning to keep them from overrunning their proper bounds. Also, since compasses were one the classical tools in geometry (along with the simple straight-edge), compasses symbolize the science of geometry, which is the basis of all of architecture, and more generally is the symbol of mankinds ability to learn about the world around us.
Thats a partial explanation, anyway. The longer a Mason thinks about the working tools of Masonry, the more and deeper meanings he comes to see in them.