Those are called thermal reliefs. When you try to solder a pin into a via that connects to a big ground plane, the ground plane will pull away the soldering iron's heat. That means the metals won't get hot enough to wet the solder and make a good solder joint.
By using four thin lines to connect the plated via to the surrounding plane of metal, you retain a conductive path, but increase the thermal resistance (the via can't lose heat to the surrounding flooded plane nearly as fast). Thus, the via, and the pin going through that via, will heat up quickly, the solder will flow, and you'll get a nice, solid solder connection.
To make them, most CAD tools will let you turn on a ground-plane/via option of some kind. Ask your senior person how to do that for your particular program.