instantons are indeed involved in nonperturbative effects : they miss every order of perturbation (think about exp[-1/x^2] at x~0)
Maybe you know what a soliton is : if you consider D-dimensional SPACE, a soliton is a localized solution of the equations of motion, with this friendly feature : it has a finite action. Typically, a kink or a breather. The very fundamental stuff, is that solitons are typically able to interpolate between different boundary conditions at infinity. At infinity, one of course expect to have the vacuum, so the soliton actually interpolates between two different vacua.
OK, now back to the instanton : this is almost trivial, an instanton is exactly the same think as a soliton, except for the fact that it sits in D-dimensional EUCLIDIAN SPACE-TIME. The way one interprets instantons, is as a tunnel effect : it "instantaneously" switches a new vacuum state for the field. That is what led 't Hooft in the middle of the 70's (if I remember correctly) to first coin the term "instanton".
The reason why instantons are so usefull in QCD, is because the gauge group, SU(3) for color, exhibits a non-trivial topology. The boundary condition at infinity for a gauge configuration can be caracterized by an integer number, which is called "Pontryagin index". This is closely related to the well-known "Chern-Simons number". It is just an integer which allow one to classify the solution. I don't know any physical interpretation for the Pontryagin index. It is really a topological charge of the field, and appears because of non-trivial mappings with different winding numbers.
The reason why instantons are considered so fundamental in QCD, is that they are able to break chiral invariance. What has been done is to consider a gaz of instantons (which is not a true solution because the equations are not linear), which is suppose to model the gluonic field, and then incorporate valence quarks into this gas. This is a very appealing model for hadrons. Besides, it is an efficient way to model hadrons.
References :
A "final exam" at NYU by Marko Kolanovic (thanx Marko !) on "Instantons and Vacuum tunneling" :
eprints.fizika.org:2101/archive/00000027/01/seminar.ps
Please read Diakonov whenever you want to learn about QCD and instantons :
nac21.uv.es/pdf/9602375
or arXiv:hep-ph/9602375 v1 23 Feb 1996 (this is the same)
A very good review on instantons by Diakonov :
arXiv:hep-ph/0212026
