Vias allow for the copper traces to pass from one side of the board to the other. You can see this easier here, learn.sparkfun.com/tutorials/using-eagle-board-layout/all Halfway down the page to the "Placing Vias" header, you can see where the drawn red line (top layer copper trace) turns to blue line (bottom layer copper trace) "via" a green circle. This green circle designates the hole (that is drilled, then copper plated) that allows current to flow from one side of the board to the other. So the copper traces don't cross. Sorry if this is too long of an explanation.
