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.
An idea is a thought or conception, a product of mental activity. A notion is an idea in the most general sense, but the term usually suggests thoughts of more fleeting, vague, or imperfect kind. Whereas an idea can be something fairly worked out or elaborate, perhaps even a plan of action (The student has an idea for how to become an engineer), a notion is more like a whim or impulse—a flurry of thought that hasn't been seriously worked out. Perhaps this half-baked quality explains why notions are so often rejected, challenged, or dismissed! When used in the plural, notions can take on a whole new meaning: small items used in sewing, such as buttons, hooks, and ribbon.