I'm looking for a non-technical definition of the lasso and what it is used for.
The LASSO (Least Absolute Shrinkage and Selection Operator) is a regression method that involves penalizing the absolute size of the regression coefficients.
By penalizing (or equivalently constraining the sum of the absolute values of the estimates) you end up in a situation where some of the parameter estimates may be exactly zero. The larger the penalty applied, the further estimates are shrunk towards zero.
This is convenient when we want some automatic feature/variable selection, or when dealing with highly correlated predictors, where standard regression will usually have regression coefficients that are 'too large'.
http://www-stat.stanford.edu/~tibs/ElemStatLearn/ (Free download) has a good description of the LASSO and related methods.
From Robert Tibshirani's (the author of the original lasso paper) page: A simple explanation of the Lasso and Least Angle Regression.