find /path -type f -exec grep -l "string" {} \;
Explanation from comments
find is a command that lets you find files and other objects like directories and links in subdirectories of a given path. If you don't specify a mask that filesnames should meet, it enumerates all directory objects.
-type f specifies that it should proceed only files, not directories etc.
-exec grep specifies that for every found file, it should run grep command, passing its filename as an argument to it, by replacing {} with the filename