I’d say for example if you create a domotic project in which you log data into your Galileo from a solar panel, light control, temperature and other things, then you could use the webserver to publish the data over a web page, so you can have access to the values measured by the Galileo from anywhere. In a real life application you could control or have a register of the energy consumption, to control the temperature of a motor or a machine, the level of moisture of the soil, to check the vital signs of a patient. Well that’s my opinion of the things you could do with it.
Going further, you can setup PhP, MySQL on the board. With PhP you can read and write text files on your board, like configuration files. And combined with HTML you can create a very user friendly interface to parameter your board and communicate with.