As far as I understand, networks illustrate the alternative histories. In which points of phylogenetic trees, the use of networks might be feasible to draw a conclusion about the history of evolution?
I recommand you to read this article : Mardulyn P, 2012. Trees and/or networks to display intraspecific DNA sequence variation? Molecular Ecology, 21: 3385-3390
I recommand you to read this article : Mardulyn P, 2012. Trees and/or networks to display intraspecific DNA sequence variation? Molecular Ecology, 21: 3385-3390
As a very rough answer: Trees are created under the assumption that there's just linear evolution, so that there's information flow from the "parents" to the "children", without any recombination. However, a network can give you additional information on recombination, homologous evolution, or lateral gene transfer. As a main caveat: a network is a test how "tree-like" your data set really is. If you see something interesting appearing, you need to check if it's a real effect you see, or if your data set is just bad.
I would add that if you have a lot of recombination (many connections between haplotypes) then it would be inappropriate to force the network into a tree unless that particular tree had very high support relative to the other possible trees.