Do you prefer using the keyboard, so you try to find out the shortcuts for everything? Does the device have a touch screen and you can't use it for some reason (e.g. It is broke)? There are users that prefer or must use a keyboard instead of a pointing device/touch screen for various reasons including those with physical limitations.
The keyboard must be able to access all links, buttons, or anything else that the mouse can be used to force something to happen. This is important for users that can't use or don't want to use the mouse for any reason. Also, those with limited or no sight can't use a mouse because they can't see the pointer.
If the keyboard can get to an object, the object must let the user move from it. If it does not, it is called a keyboard trap. For those using screen readers, a usual suspect is a popup window when
The order that the keyboard tabs to items on the Webpage makes sense. Usually the default order is okay. Sometimes Web developers will change the order of the tab stops using an attribute and it can produce what appears to be an erratic order.