People buy cards because they have sentimental value and they mean more than just an object. 

Besides having a heartwarming message a card can also connect with someone on a personal level depending on what is on the front. Cards can be kept on display so you are constantly reminded that someone cares for you so people buy them.

 

People buy cards for children to write for somebody or for themselves so that they can read the message, this can improve their reading and writing skills. Cards can be viewed as a gift also so if somebody doesn't have the money to buy someone a gift they can buy them a card instead.

It's a common way to save money and make someone feel important.

Some People buy cards when they don't particularly want to, like sending it to a boss you don't like for example. It is a sign of respect in some way and people buy it because they feel they haft to.