The chi-square test is a statistical test of independence to determine the dependency of two variables. It shares similarities with coefficient of determination, R². However, chi-square test is only applicable to categorical or nominal data while R² is only applicable to numeric data.
From the definition, of chi-square we can easily deduce the application of chi-square technique in feature selection. Suppose you have a target variable (i.e., the class label) and some other features (feature variables) that describes each sample of the data. Now, we calculate chi-square statistics between every feature variable and the target variable and observe the existence of a relationship between the variables and the target. If the target variable is independent of the feature variable, we can discard that feature variable. If they are dependent, the feature variable is very important.
Mathematical details are described here:http://nlp.stanford.edu/IR-book/html/htmledition/feature-selectionchi2-feature-selection-1.html
For continuous variables, chi-square can be applied after "Binning" the variables.
An example in R, shamelessly copied from FSelector
# Use HouseVotes84 data from mlbench package
library(mlbench)# For data
#Calculate the chi square statistics
weights<- chi.squared(Class~., HouseVotes84)
# Print the results
# Select top five variables
subset<- cutoff.k(weights, 5)
# Print the final formula that can be used in classification
f<- as.simple.formula(subset, "Class")
Not related to so much in feature selection but the video below discusses the chisquare in detail https://www.youtube.com/watch?time_continue=5&v=IrZOKSGShC8