When you shamble down the street, you move slowly and shuffle your feet. People who shamble along are usually tired, elderly, or sad.
An exhausted hiker might shamble along the final mile of trail after weeks of walking, and your grandfather might be the speediest one in his nursing home, passing up the residents who shamble along with their walkers. A kindergarten teacher might call to her class, "Don't shamble! Pick up your feet and let's go to the library!" Shamble probably comes from the outdated adjective that means "ungainly or awkward."