The noun influence refers to a type of unofficial power to direct the actions or thoughts of others; it typically implies deference to one's character, ability, or station. The noun leverage also refers to a type of power, but power of a less mysterious nature, usually derived from an advantage. A company that has the advantage of being the only commercial enterprise in a town might have considerable leverage, or power, in its union negotiations. Leverage comes from the word lever, a rigid bar used to move an object by applied force at a certain point. Perhaps unsurprisingly, the word leverage commonly appears in discussion of politics and business.
Something that is easy is by definition not hard or difficult. When an activity or goal can be carried out or achieved with little difficulty or effort, it may be called facile. A facile victory, for instance, is a victory won handily with minimal exertion. Similarly, someone who is facile with words expresses themself with ease. While these senses of facile connote skillfulness, facile sometimes sports an air of superficiality: facile answers are overly simplistic or trite responses to difficult questions; facile assumptions are things taken for granted that really shouldn't be; and facile arguments are shallow lines of reasoning—all things formed or arrived at a little too easily.
When we understand something, we perceive the meaning of it. When we fathom something, the perception goes a little deeper. To fathom something is to penetrate to the truth of it, or plumb its depths. The word gets its depth, so to speak, from the noun sense of fathom, a unit of measurement equivalent to six feet used for gauging depth in water. Consequently, one can fathom (measure the depth of) a body of water, or fathom (attempt to get to the bottom of) a difficult or complicated matter. Such depths may seem profound and hard to comprehend, which is perhaps why fathom is so frequently used when full comprehension feels just out of reach.