To spur something on is to get it going, to encourage it, to hasten it or stimulate. Cowboys wear spiky metal tools called spurs on their boots to kick their horses and spur them to greater speed.
Economists talk of lowering interest rates to spur spending. A new source of funding for research will hopefully spur new proposals for research from scientists. An earthquake in China might spur cities in California to a higher standard of earthquake preparedness. You might spur your team on to victory by cheering from the sidelines.