I made a slight change to my website and changed the title and description, so far I have not seen any changes in google. Will google update decription of my website? If yes how long would it take?
At some point they will but no one knows when. Higher PR pages (PR4+) tend to get Google to react quicker but it's no guarantee that they will do anything quickly at all. Also, Google prefers to use the DMOZ description for many sites so it's possible if that is what they are currently using then you will not see a change in your description at all.