If you can provide some sound reasoning that touches on tertiary structures of proteins and does not use a lot of advanced chemistry jargon that might be really helpful, especially for an intro biology student. I think my problem is that activation energy is lowered by an enzyme and I know how its like on the Gibbs Free Energy diagrams. However I think I've been taking this as an axiom and I'm not really sure why.
We should first understand what activation energy really is and what does Arrhenius equation mean. For any chemical reaction to happen you need to break some existing bonds in order to form new bonds. Breaking existing bonds consumes some energy; in other words you have to convert the reactant to an active form which undergoes a reaction readily. The energy that is required to do so is called activation energy.
It is essential to note that activation energy is an empirical term because it does not actually consider the reaction mechanism. The above example of bond-breaking and re-formation can happen in many ways. Some mechanisms may require less activation energy than the others.
The Arrhenius equation denotes the relationship between reaction rate and activation energy:
where $k$ is the reaction rate constant, $A$ is the Arrhenius constant (an arbitrary proportionality constant), $E_a$ is the activation energy, $R$ is the universal gas constant and $T$ is the absolute temperature.
This equation tells you that the rate of reaction decreases with increase in activation energy and increases with increase in temperature.
The temperature indicates the internal energy of the system i.e. the movement of molecules. Collision between molecules is essential for chemical reaction to happen and increased temperature increases the chance of collisions (due to higher molecular movement).
How do enzymes lower activation energy of a reaction?
They either do that by increasing the chance of interaction between the reactants or diverting the reaction to follow a different mechanism that has a lower activation energy.
As you know, the enzyme binds to the reactants and forms a complex. This effectively brings the reactants closer thereby increasing the probability of their "collision" which in turn increases the reaction rate. This can be further extended to the level of molecular orientation. The analogy presented by AMR in their comment is great. It is one of the mechanisms by which the free energy of the system would increase — by reduction of entropy. Clamping the substrate in place can expose its reactive groups to the co-reactants, thereby allowing the reaction to proceed faster.
In most other mechanisms of enzyme catalysis, the functional groups in the enzyme active site react with the substrate to form intermediates and these intermediates which have lower activation energy give rise to product faster than the substrate in absence of the enzyme.
It is to be noted that this entire process of catalysis adds a few extra steps to the actual reaction (binding, formation of intermediates etc). The catalyst would be effective only if these combined rates are still faster than that of the uncatalyzed reaction.