I have the impression that Woody1 is making a genuine effort to understand the science. I'll address the OP directly:
A 270ppm to 400ppm CO2 concentration is important because of several reasons.
1. CO2 has a long "residence time" meaning that it takes a long time (~5 years) for a molecule of CO2 to be absorbed back into the a solid or gas, or more generally rendering it in a state where it cannot absorb heat radiation. A spike in the concentration of CO2 will take hundreds of years to return to normal. Water vapor is different, because it doesn't stay in the atmosphere for as long. Pointers: The molecular ~5yr estimate can be traced back to Craig (1957) or earlier. Global climate models (GCMs) started around that time, maturing with enough power by the mid-80s by Hansen's work to predict our current situation. It is through these GCMs, also with ocean-atmosphere interaction work by Revelle and Suess (1957), that people now know the collective residence time of CO2 in the atmosphere.
2. The unique infrared absorption bands of CO2 relative to water vapor, the dominant greenhouse gas, means that CO2 will always absorb IR at any increased concentration and never saturates out. Millions of these absorption lines are now known, and this information is stored in Harvard's HITRAN database, which I think is accessible to the public. The "golden age" of this spectroscopy was around the 1950's when heat-seeking missiles were developed by the U.S. military. A few physicists - Plass (1956, 1958), Manabe and Wetherald (1975) used them for climate computations.
3. The energy gained by the earth from the extra IR absorption is only 1-2 W/m^2, which is small compared to net 300-400 W/m^2 on a sunny day. But that really does add up over the years and one can't expect nothing to happen over decades. The effects on weather, which is more unpredictable than climate, is the emergent development of more extremes. There's a good paper on this topic by Hansen et al. (2012). This happens all the time across many different areas of science including my own past research on engineering. A statistician would call this "heteroscedasticity," and a statistical physicist would draw analogy to the Boltzmann distribution for molecular velocities in a heated gas.
I know there are many, many references for each of the three points made above, but sometimes it's hard to find simple facts in the academic literature even from Google Scholar. In my opinion, the IPCC summarizes the science very well. For more technical information, it's probably best to consult someone working on the topic. Just keep looking and be persistent.
Link to a good video on the topic. (I've met this guy before).