[[ is bash's improvement to the [ command. It has several enhancements that make it a better choice if you write scripts that target bash. My favorites are:

It is a syntactical feature of the shell, so it has some special behavior that [ doesn't have. You no longer have to quote variables like mad because [[ handles empty strings and strings with whitespace more intuitively. For example, with [ you have to write

 if [ -f "$file" ]

to correctly handle empty strings or file names with spaces in them. With [[ the quotes are unnecessary:

 if [[ -f $file ]]

Because it is a syntactical feature, it lets you use && and || operators for boolean tests and < and > for string comparisons.