What is light localisation? Reading about plasmonic nanoparticles I faced the term "localised light".
How can one localise light? What are applications of it?
 A: One way to obtain localisation of light is through Anderson localisation in disordered media, see https://en.wikipedia.org/wiki/Anderson_localization. It is a subtle effect but has been verified experimentally. The theoretical description is also pretty complicated. 
A: I will try to give a simple answer without going too deep into physics details. Localization of light is the confinement of a light wave so that it is very intense in one particular location. Usually it vanishes rapidly as you get farther away from that location.
(Note that by "light wave" I am not talking about the traveling plane waves that you would use to describe a light beam; this is more of a stationary oscillation mode.)
This crops up in the context of plasmonic nanoparticles because surface plasmons' wavelengths are smaller than normal light waves of the same frequency, allowing surface plasmons to be confined into even tinier spaces.
There are two major advantages that lead to applications. One is that confining the light into a small space allows easy manipulation of it, for example by tailoring the shape of your nanoparticle.
The other is that confining the light into a small space also squeezes all the energy it carries into that small space. This is called field enhancement. You can then do processes that require a lot of electric field strength (e.g. nonlinear things) without needing a huge amount of light to achieve that field strength.
(I adapted some of this answer from the introduction to my doctoral dissertation.)
