Yarn or thread strands that are left after fastening off are woven in to secure them, to prevent unraveling over time.
Image copyright 2007 by Sandi Marshall, licensed to About.com, Inc.
Upper Photo: Use a large-eye yarn needle. Thread the yarn end onto the needle and weave the needle under the stitches for two inches or so. Pull the yarn through.
Lower Photo: Then, skipping half of the last stitch woven under, weave back through the same stitches for about one inch or so. Pull yarn through. Cut the yarn close to last stitch woven under, so end will "hide" under this last stitch.
Where Do These Ends Come From?
Leaving A Length At The Beginning: When doing your starting chain or when adding a new color while crocheting, always leave a length of about six inches or so before your first loop of starting chain or before your first stitch in the new color. This length is woven in when you are finished with your project, so that the end will be secured to guard against unraveling over time.
Leaving A Length At The End: Also leave a length at the end of your project or at any time that you join a new skein because you have run out of yarn or are finished with a certain color.