Does it mean that they are the most involved people in email correspondence?
I am not sure what exactly you mean by involved, but I can’t think of a definition for which I would agree with this.
If by involved you mean the person communicating with most other people or sending or receiving the most e-mails, you can simply evaluate this directly.
In network terminology, this would be the degree or out- or in-strength of the network, respectively.
As a simple and extreme counter-example, consider a network split into two well-connected sub-networks with only one person communicating with members of both networks. This person will have one of the highest closeness centralities, usually the highest. However this person could have gotten there with little involvement. Details depend on how exactly you define connections and the closeness centrality, but in the extreme case, two e-mails would have sufficed.
Or there is another interpretation of that result?
If you didn’t thoroughly and intelligently prune your dataset, my default assumption would be that these nodes are pathologic but boring cases, such as prolific spammers or administrators.
For example if you make such a network for a department at a university, you will likely find the centre to be some secretary who is charged with informing everybody about upcoming talks.
On the other hand if you do such a pruning, you’ll probably need to investigate beyond the pure network data and find your answer anyway.
If we assume that your network is a meaningful proxy for social connections, the interpretation is quite directly the definition of the closeness centrality: The most central person is the one who is (socially) connected other person with the fewest in-between steps. What this exactly means, depends on the nature of your network. For example, in a terrorist network organised into cells, this would probably be the leader. But this interpretation does not translate well to other cases.