Swarm intelligence is a field of biologically-inspired artificial intelligence based on the behavioral models of social insects such as ants, bees, wasps, termites, etc. A Swarm is a configuration of tens of thousands of individuals that have chosen their own will to converge on a common goal. It is the Complex Collective, Self-Organized, Coordinated, Flexible and Robust Behaviour of a group following the simple rules.
There are real-world applications that are based on SI are those that often required coordination and cooperation techniques, optimization process, exploratory analysis, dynamical problems, etc. Some of these are:
Optimization techniques (mathematical functions for example)
Coordination of a swarm of bots(to organize inventory for example)
Routing in communication networks. (This is also dynamical combinatorial optimization)
Data analysis (usually exploratory, like clustering). SI has a lot of applications in data mining and machine learning. This permits the SI algorithms to find interesting patterns in big sets of data.
NP problems in general
I'm sure there are a lot more. You should check the book:
"Swarm Intelligence: from natural to artificial systems".