When you delete a file, the operating system does not actually erase the file. Instead, it just removes some references to the file, so that other files can re-use the same areas previously occupied by the file. Until new files get the chance to be written exactly in the same place, anyone can see and recover the old data.
A secure erase will overwrite the areas previously occupied by the file you want to destroy, with random data, so that the old data is no longer accessible.