It's getting a bit late, I can reply tomorrow in greater detail if you want, unless someone else comes up with a detailed answer before that. But the the general gist is that the carbon cycle of plants is.. well.. a cycle. Most of the CO2 that is removed from the atmosphere by photosynthesis of plants is eventually returned to the atmosphere. As plants die the organic matter they produced will decompose - aerobic decomposing/digestion produces CO2 and anaerobic produces mainly methane. And methane eventually reacts with oxygen to form CO2 and water.

Some amount of carbon gets deposited in the soil permanently (eventually forming things like coal and oil), but that's a relatively minor part of the carbon cycle on land.

However by increasing the total amount of living plant biomass you do decrease the amount of CO2 in the atmosphere. Then all we gotta do is take all those plants and shove them deep underground so that the carbon is removed from the active cycle.. reverse mining, heh.