The shake&strain technique is used to combine and chill three or more ingredients (with some exceptions), to be served without ice. Pour the ingredients into a boston shaker with ice, shake vigorously for about ten seconds, open the shaker and pour the contents into the glass, retaining the ice with the strainer.
Check out the recipe for cosmopolitan.
One more tip
When using the boston shaker, the large mixing tin should always be turned towards the customer in order to prevent splashing the customer in case the shaker is not properly closed.