There are several things that stop your kitchen sink from draining. The more common causes are food debris from your garbage disposal. A good way to avoid this is to only put small amounts in when using the garbage disposal and most importantly, run lots of cold water after the disposal is turned off (60 seconds).

Another contributing factor is grease and soap build up. If you have an older house, say over 35 years old, and you’ve never had your drains serviced, there is a good chance that your pipes have build up in them.
It’s a good idea to have your drain piping mechanically cleaned and re-stored about every 20 years. (Don’t you wish your car could go this long without maintenance!) A Rooter-N-Drains technician can quote you on a whole house drain rejuvenation that will restore your drains to an almost new condition. And they can usually get it done in less than a day. Along with a mechanical cleaning, your kitchen, laundry and main sewer line will be scoured clean with high pressure water.
After all the drain cleaning is complete your system will receive it’s first treatment of our environmentally safe "Drain Maid". This is a bio product designed to eat away at all the grease and soap after a drain cleaning. To keep your drains open, your lines should receive regular maintenance treatments with Drain Maid.