I always get a chuckle out of how terminology and/or phrases in sports are so simple with very little creativity but it is something I do appreciate. Just like the phrase, "long swing", it describes the issue very clearly. The swing is long and, for most hitters, this is not a good thing.
What makes it a long swing?
There are two components of a long swing. One of them is what is called "casting out". Casting out is where the hitter "casts" the bat head early in the swing.
Another way of saying it is when the bat head gets away from the body early in the swing. You can see the girl to the right where her barrel/bat head is really far away from her body early in the swing.
The phrase, "staying inside the ball" was created to help the hitter work on not casting out. The phrase basically means to keep the hands and barrel inside the path of the oncoming ball as long as possible.
This video is a really good description of what is going on with casting out. I also think the drill is a decent drill to help teach this skill.