In Data Mining, what does it mean to be greedy?
I'm not a Data Mining expert, but from what I understand, it means the same thing as it does outside of data mining: to improving the solution in a locally optimal way, rather than one that is guaranteed globally optimal. (And, as Raphael comments, to not backtrack on that decision).

For example, if you are training a graphical model, the process of repeatedly adding the edge that improves your model's fit the most, until no changes improve the model, is a greedy process. at each stage, you've taken the action which has the most incremental improvement over your current model, but the result may not be globally optimal.

Likewise, in the clustering example, to say that the clusters are merged greedily means that they are merged in the way that provides the best incremental improvement over other merges, but may not lead to the optimal clustering at the end.