Imagine a kid kicking a can - an empty beer can or such. It's noisy, disruptive, not something "nice children" do. Now, "all over the place" - everywhere around, through the neighborhood. Lots of noise, lots of cheek as it surely annoys many people - being noisy, obnoxious and disrespectful - a spunky young troublemaker, still not strong enough to cause any real damage, but obnoxious already.
This is the image the song is painting in the first stanza - a kid that "will be a big man some day", not just grown up, but influential. Then it proceeds to a young revolutionary (that will 'take on the world some day') and ends with a disillusioned, tired old man only seeking peace.