Particle で indicates that the preceding noun is a means of doing something(i.e., the desired action is achieved by using Ｎ). Here, it marks a means of transportation. The phrase あるいて(by walking) is also presented here, although it is different in form. This verb form is called the Te-form and will be introduced in Lesson 10.
うちから えきまで バスで いきます。
I go from my house to the station by bus.
えきから がっこうまで あるいて いきます。
I go from the station to school by walking.