They were not first. The one who was ahead of them was ahead by a large distance. A close second would mean that the first and second are not separated by much. This school is the best in the area, but the one down the road is a close second. This school is the best in the area. The one down the road is a distance second, not nearly as good.

Suppose you finished first in a race, and I came in second. But you crossed the finish line long before I did, and I only came in second because all the other contestants were even slower than I was. You won first place, I was "a distant second."

Here is an example, hope can help you to understand: if people are running a race, the runner-up comes in 10 minutes later after the winner, they would be a "distant second." If the runner-up comes in a very short time like few second after the winner, they would be a "close second."

It is used to describe the position of a contestant (or the rank of anything involved in a race) which is very far away from the first position. It also suggests that the contestant was never in danger of catching up with the first.