Connecting flights are fine if the first flight segment is not delayed.
You check your bags at your airport of origin all the way to your destination.
At any of the major hubs in the United Sates, when flying on domestic flights on a single airline, there's no need to go through a security check at your connecting airport.
At your connecting airport, your departure gate might be right by your arrival gate, or you might have to go to another concourse. At larger airports, there are often subways, PeopleMovers, moving sidewalks, or shuttle vans to help you.
It's a chance to stretch your legs, use a restroom that's not an airplane lavatory, and have a meal, if you have enough time.
But that brings us back to my opening line: Connecting flights are fine IF the first flight segment is not delayed. With a tight connection, even a relatively short delay can be a problem. That's why, if I need to connect, I prefer to have more than hour, preferably two hours. I've missed connections in the past, and it's no fun waiting all afternoon for another flight.
By the way, if the delay is due to weather at the connecting airport, arrivals and departures can both be delayed. In that case, you can often still make your connection, even if you first flight is delayed.