The web page you linked uses term Spatial resolution. It is to describe the resolving power of the imaging device they have up there, i.e. the ability to separate points of an object which in this case is the surface of the Earth.

Ten meters resolution tells us that the camera located 685 kilometers above sea-level is able to tell apart objects that are 10 meters from each others. On a dark surface of a parking lot two lightcolored cars will appear as single pixel if they are closer than 10 meters to each others. More than 10 meters apart the cars will produce two pixels on the image.

What the 10 meter resolution means on your computer screen? I presume you have a wide screen display of 1920 pixels horizontal. The 10 meter resolution means that if you go "pixel peeping" the image, you will see 10 meters of Earth surface per each pixel on your display, resulting in 19,2 kilometers wide patch of ground if you view it on full screen. However they say on that wikipedia page that the imaging device is able to capture a 50 kilometer wide patch of land as the satellite moves across the sky. This you divide with 10 meters to get the horizontal resolution of the imaging sensor they have.

50 km is 50.000 meters divided by 10 meters equals 5000 pixels wide sensor. Now, that is a number we can understand easily. In real life it might not be as simple as that, but I believe this already answers your question.

A sample of 10 meter resolution imagery: Central Kalimantan maximum resolution

In the rightmost picture you can easily see a wide river and a narrower river come together, and supposedly farmlands divided into rectangles by a crisscross of ditches, and some white blobs that are clouds. The methods and objectives are explained at http://www.eorc.jaxa.jp/ALOS/en/guide/forestmap_oct2010.htm