I will briefly touch on the "speculative" part of masonry.
At the left and right side of the worshipful master, there are two stone blocks called ashters. One is smooth edged and perfect. The other is known as the rough ashter. They symbolize the human being. The rough ashter is us. In our rough form. Before being brought to light (you are blindfolded in part of the ritual. 'In the beginning there was darkness, and then God said, let there be light! You are then unblindfolded, and the masons have positioned their bodies, hands, and feet, in a specific way to show different aspects of sacred geometry, advancement of the mind and spirit, and something else, which is very important, and I will touch back with it later)
After you are brought to light, you are handed working tools of an operative mason, which includes the gavel, square, and plumb.
You then symbolically apply the teachings of these tools to yourself, smoothing out the rough edges and building your body more fit 'for that house not made with human hands, eternal in the heavens'
The square is so you remember to 'square your actions' by thinking of the reactions that will affect NOT yourself but others first, then how it affects you second. The plumb (used to measure interior angles and make sure things were straight) so that you may walk upright among your fellow man, and not have any actions which would make you ashamed of them, or make others ashamed of you. The common gavel is used to break off rough corners on stones, making them smoother and more fit for use.
After you go through the first degree, one begins to see how symbolically they can apply the teachings and become better men and better humans. Smoothing out the rough parts of their soul.