Most force-directed layouts use to generate hairballs when facing large and highly connected graphs as such highly connectivity makes most of the nodes in the network to pull each other creating very cluttered and difficult to understand representations.
Hive plots attempt to solve this problem by providing a set of axis upon which nodes of the graph can be ordered according to a specific measure or centrality. Edges are then drawn as Bezier curves, which can be color coded to provide further information about the relation between nodes.
Nodes are located along an axis decided by the user according to a specific measure or centrality while edges between them are drawn using Bezier curves (image taken from http://www.hiveplot.net/).
According to the authors:
hive plots are excellent at managing the visual complexity arising from large number of edges and exposing both trends and outlier patterns in network structure
To me, one of the most important features of this visualization is that it creates deterministic graph visualizations, meaning that, contrary to what happens with force-directed layouts, the graph structure remains unaltered between algorithm runs.