Let's review some facts (this part of my explanation requires memory, but you should already know this from lecture)
#1: The ciliary muscle is similar to sphincter muscle, because when ciliary muscle contracts, the opening in the center becomes smaller; when it relaxes, the opening is as wide as it can be.
#2: The lens is located in the center of this circular ciliary muscle. The lens sits in a bag called capsule, and this capsule is connected to the ciliary muscle by zonules.
Now let's answer your question (this part of my explanation is simply applying the facts we know)
When the circular ciliary muscle relaxes, the tension is put on zonules which pulls on the capsule. Since the capsule is stretched out due to this tension, the lens is squished and flattened to a certain degree. The next line of reasoning requires more physics to understand so it's better to remember that thin lens increases your distance visual acuity.
Accommodation is the opposite process. The ciliary muscle contracts and, therefore, makes the opening in the center smaller (much like a sphincter in fact #1). Narrowing of the center opening in turn relaxes the zonules and capsule. As a result, the lens becomes thicker than what it is otherwise (see preceding paragraph for reference). Again, physics tells us that thicker lens increases your near vision.