This algorithm uses the p-value in a combination of forward selection and backward elimination.
You can find out more at: NCSS Statistical Software Step-wise Regression write-up
The lower the p-value the higher the variable's rank.

This algorithm uses the p-value to conduct backward elimination.
The variable with the highest p-value above the critical alpha value is eliminated from the model during each iteration.
You can find out more at: NCSS Statistical Software Backward Step-wise Regression write-up
The lower the p-value the higher the variable's rank.

This algorithm uses the p-value to conduct forward selection.
The variable with the lowest p-value lesser than the critical alpha value is selected to be in the model during each iteration.
You can find out more at: NCSS Statistical Software Forward Step-wise Regression write-up
The lower the p-value the higher the variable's rank.

This algorithm uses the Akaike Information Criterion (AIC) to evaluate if the inclusion/exclusion of certain variables would give the best-fit model.
AIC captures the trade-off between goodness of fit and complexity of a model.
You can find out more about AIC at: University of Wisconsin - Explanation on AIC
The lower the AIC value the higher the variable's ranking

This algorithm uses the Akaike Information Criterion (AIC) to evaluate if the exclusion/elimination of certain variables would give the best-fit model.
AIC captures the trade-off between goodness of fit and complexity of a model.
You can find out more about AIC at: University of Wisconsin - Explanation on AIC
The lower the AIC value the higher the variable's ranking

This algorithm uses the Akaike Information Criterion (AIC) to evaluate if the inclusion/elimination of certain variables would give the best-fit model.
AIC captures the trade-off between goodness of fit and complexity of a model.
You can find out more about AIC at: University of Wisconsin - Explanation on AIC
The lower the AIC value the higher the variable's ranking

cForest uses a Conditional Variable Importance Measure for Random Forests and is based on unbiased conditional inference trees.
cForest follows the principle of 'mean decrease in accuracy' importance.
The higher the drop in the mean decrease in accuracy the more significant is the variable.

Random forests averages out multiple deep decision trees, trained on different parts of the same training set, to overcoming over-fitting problem of an individual decision tree and thereby provide the importance of each variable.
For Regression, the random Forest importance is based on the 'mean decrease in node impurity' principle which is measured by the residual sum of squares.
You can find out more about random forests at: A comprehensive write-up about random forests
The higher the node impurity, the more significant the variable.

Lasso or Least Absolute Shrinkage and Selection Operator, is a procedure that improves the prediction accuracy and interpretability of regression models by altering the model fitting process to select only a subset of the provided covariates.
Lasso is a continuous subset selection algorithm, that can 'shrink' the effect of unimportant predictors, and thereby can set effects to zero.
Use lambda.1se when you want to select lambda within 1 standard error of the best model.
Use lambda.min when you want to select the lambda with minimum mean cross-validated error.
You can find out more about the Lasso Procedure at: A comprehensive write-up about the lasso net procedure
Lambda is the weight given to the regularization term (the L1 norm), so as lambda approaches zero, the loss function of your model approaches the OLS loss function. As you increase the L1 norm, variables will enter the model as their coefficients take non-zero values.

Elastic net is a hybrid of ridge regression and lasso regularization.
Like lasso, elastic net can generate reduced models by generating zero-valued coefficients.
Empirical studies have suggested that the elastic net technique can outperform lasso on data with highly correlated predictors
Use lambda.1se when you want to select lambda within 1 standard error of the best model. Recommended for Elastic net.
Use lambda.min when you want to select the lambda with minimum mean cross-validated error.
You can find out more about the Elastic Net Procedure and its difference from Lasso Procedure at: Stanford University - Slides explaining the elastic net and lasso procedure
Lambda is the weight given to the regularization term (the L1 norm), so as lambda approaches zero, the loss function of your model approaches the OLS loss function. As you increase the L1 norm, variables will enter the model as their coefficients take non-zero values.

Boruta algorithm uses variable importance obtained from random forest along with randomisation to obtain the truly important and statistically valid variables for a model.
As boruta is based on random forest, it too uses the 'mean decrease gini' to calculate the importance of each variable.
You can find out more about the Boruta Algorithm at: A comprehensive write-up about the boruta algorithm
The higher the importance the more significant the variable.

Random forests averages out multiple deep decision trees, trained on different parts of the same training set, to overcoming over-fitting problem of an individual decision tree and thereby provide the importance of each variable.
For Classification, the random Forest importance is based on the 'mean decrease in node impurity' which is measured by the Gini Index
You can find out more about random forests at: A comprehensive write-up about random forests
The higher the node impurity or Gini Index, the more significant the variable.