A couple weeks ago I got very excited by the idea that the name for our historical priests ("Levi") was very similar to "Lah-vi", which means "my heart". Further research dispelled this notion; there are two letters that make the "v" sound, and the similarity of the two is merely coincidental, not indicative of a linguistic link. Still, the idea intrigued me enough that I wanted to spend some time playing with it.
Following the link in one direction, the priests become the heart of the community. The vital organ that keeps blood and life flowing through our communal body. While the modern rabbi is very different in many ways from historical priests, this part remains the same. More than leading prayers, more than teaching the youth, the rabbi's job is to keep the vital energy flowing through the congregation, spreading prayer, education, and administration where they are needed like nutrients through the bloodstream.
Moving in the other direction, I love the image that each of us has our own personal priest residing in our chest. We do not need external clergy to regulate our connection with the divine; we can create prayers, interpret the law, and talk or listen to god all on our own. This is the voice inside us that reminds us what is right and what is wrong. Beyond the written Torah and the oral Torah we have this inner Torah; we study the others just to remind ourselves of what our hearts already know.
It's probably because of my love of puns, but I am less willing to believe in pure coincidence than most scholars when it comes to words sounding alike. Granted, every language has words they assimilated from other cultures, which greatly heightens the evidence for "coincidence", but one of these terms is a name. That means at some point someone said, "I like the way this word sounds! I want to be called that for the rest of my life." Someone else, knowing the meaning of the name, chose it for their child. Interestingly, the name "Levi" is translated as "joining"; some sources attribute this to Leah's desire for Jacob to join with her. Even if it is a coincidence, there is a very pleasing resonance between "joining" and "my heart".