What's wrong with existing inner class, why inner class can't be used for representing closure?
Currently I will post here some resources to start with.
First of, below is listed great overview what is closure is. It is language agnostic. I recommend to read it Closure http://martinfowler.com/bliki/Closure.html
ADDED A BIT LATER
[January 2007] A Definition of Closures http://gafter.blogspot.com/2007/01/definition-of-closures.html
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[December 2011] State of the Lambda http://cr.openjdk.java.net/~briangoetz/lambda/lambda-state-4.html
[October, 2007] Advanced Topics In Programming Languages: Closures For Java http://www.youtube.com/watch?v=0zVizaCOhME
[January 4, 2011] JSR 292 goodness: Lambda to SAM type conversion using invokedynamic http://weblogs.java.net/blog/forax/archive/2011/01/04/jsr-292-goodness-lambda-sam-type-conversion-using-invokedynamic