How to explain difference between v&v give the example

Have you ever prepared an "Egg Omelette"! I am assuming that you have prepared. So how will you prepare an "Egg Omelette"? You will try to get all the ingredients required for making an "Egg Omelette" like - eggs, oil, salt, onion, and the other ingredients if any! Then what will you do? You will "verify" the ingredients and see if they are of good enough "quality" and in proper "quantity". Won't you? Here you are doing Verification.

Now let me assume that you have prepared "Egg Omelette". Now will you directly serve it to your guests? Or you would like to "taste" it to see if it has been prepared well? A good cook will choose to taste the dish before serving it to guests. This is comparable to Validation.

Difference between Smoke testing or Sanity testing

Sanity Testing:
Sanity testing is used to test in intial check up is made on the build after recieving from developer.
Sanity Testing:When a major bug is filed in a build,developers will fix that particular bug alone and releases a new build ,testing the new build to check the particular issue is fixed and fixture has not caused any impact on other functionality,is known as "Sanity Testing"

Smoke Testing
In this we test that application is able for the further testing or not. We just check the capability of the application for testing.
We can check following things in this:
i)Build is properly installed on the system( because sometimes application crash during installation of the application).
ii)Installed application properly connected with the database and network.
iii)All the module are display and working fine.

Boundary value testing

is a technique to find whether the application is accepting the expected range of values and rejecting the values which falls out of range.
Ex. A user ID text box has to accept alphabet characters ( a-z ) with length of 4 to 10 characters.
BVA is done like this, max value:10 pass; max-1: 9 pass;
max+1=11 fail ;min=4 pass;min+1=5 pass;min-1=3 fail;
Like wise we check the corner values and come out with a conclusion whether the application is accepting correct range of values.