I am rather fond of the various brews made by Yuengling. They’re brewery is in PA, and they have distributors along the east coast from New York to Florida. My current living quarters are in CT. I do not see Yuengling in any of the stores. I checked the website. http://www.yuengling.com/distrib.htm shows that there is no distrubutor of Yuengling in CT. Does this mean I cannot purchase it here? I don’t really understand what a distributor does. Can I (legally) purchase it in NY and bring it back to CT? Is the ATF going to burn my house down if I do that?
Yes, you can take it back.
The distributor buys the brew from the brewery, then ships it to either a shipping site, or directly to retail outlets.
You’re fine to bring it back from NY. Just wait till you get home to start enjoying them. 
The ATF won’t care, but the Connecticut State Police might. IIRC, from my few years living there, Connecticut is one of the states that doesn’t allow an individual to bring any alcoholic beverages into the state from another state. It’s mostly a tax thing of course.
In reality though - don’t get pulled over for something stupid that gets your car searched, and no one will ever know that your Yuengling is contraband.
It’s not technically legal, no. Most people will look the other way.
I live very near to the border between Missouri and Kansas. There are some beers (sadly, Yuengling is dist. in neither state) that are only available in Missouri.
A cop that came to speak to a beverage control class that I took told us stories of the time he used to camp on the Kansas side of State Line road and wait for people to turn left out of the liquor store on the Missouri side (to get to the highway that takes them into the city on the MO side) but since they had crossed the center line, they were in violation, got tickets and confiscated all their booze.
It DOES happen, but it’s not very likely.