The main idea of this exercise is to use a back-end service via its API and build the front-end to display the data to the user. You can use JQuery, Javascript, CSS and HTML in this project.
The first step is to register in the Weather System via http://www.wunderground.com/weather/api/
Then you need to understand the API, this type of API is called RESTfull, this means that you can call any function of the API using a single URL and the system will reply with data (most of the time in JSON, but it could be in XML).
Read the documentation of the API here: http://www.wunderground.com/weather/api/d/docs?MR=1
Using HTML, CSS, JavaScript and JQuery, build a SPA (http://en.wikipedia.org/wiki/Single-page_application) that will let you to enter a city and then will present you relevant data concerning the city´s weather forecast.
The user should be able to change of city and to define if he wants to see the data on Celsius or Fahrenheit.
You are free to add as much features as you want to this SPA, and the best application will win a special award.