I think it can be a combination of a few things, but dumb none the less. For instance, a lot of people do office lottery pools and that gives them a sense of community and the dream of perhaps someday getting out of the rat race. With 15-20 other people in your office pooling tickets, your odds of winning slightly increase.
Then there is the idea that the media will parade around the lucky ones who do win, making them more visible/relate-able and in essence convince people that they can be the next lucky winner.
On top of those two, each lottery ticket only costs a few dollars, which makes it easy for people to part with their money. Even though many people will play the lottery for years and accumulate big losses, when they are small losses each time it is much easier to deal with than say losing several thousand dollars at one time