At first glance, nudging an asteroid closer to Earth seems like one of those "what could possibly go wrong" scenarios that we generally try and avoid, and for good reason: large asteroid impacts are bad times. The Chinese, though, seem fairly optimistic that they could tweak the orbit of a near-Earth asteroid by just enough (a change in velocity of only about 1,300 feet-per-second or so) to get it to temporarily enter Earth orbit at about twice the distance as the Moon. The orbit would be unstable, and eventually (after a few years) the asteroid would head back out into space from whence it came, but it would stick there long enough for us to poke around on it.
While the Chinese are likely going to start small (the prime candidate right now is a 30-foot-wide rock), they're thinking bigger. Much bigger. Like, over a mile bigger, since a metallic asteroid that size would be worth an absolutely staggering amount of money. Now, were something to get screwed up and that mile-wide metallic asteroid hit Earth instead, we'd be looking at something like a 24-mile-wide crater and a fireball so large that trees 200 miles away would spontaneously burst into flames, among other fun effects.
But let's just assume that these Chinese science dudes know exactly what they're doing and that they'll be able at some point to nudge one of these huge asteroids into temporary Earth orbit. Then what? Well, there's science to be done of course, but they estimate that a two-kilometer-wide metallic asteroid (about 1.2 miles across) could be worth something like 25 trillion dollars, which would handily pay down the entire U.S. national debt with barely enough left over to restart the space shuttle program. Sweet! Except, sweet for China. Not us. Oh well.