Due to the fast carbon cycle, there is natural variation in levels of CO2 throughout the calendar year. Because plants take in CO2, one would expect the level of CO2 to be lowest when plants are thriving (in the summer) and highest when most plants are dormant or dead (in the winter). However, CO2 takes a while to disperse across the entire atmosphere of Earth; one CO2 molecule takes about two years to travel around the Earth and become fully mixed. Therefore, there is a delay between when we would expect to see the most CO2 and when the peak actually occurs. CO2 levels peak in spring, after a winter of plants not taking in CO2, and the levels are lowest in the fall, after a summer of plants using a lot of CO2.
Natural variation also occurs according to location. The norther hemisphere has more land and more plants, and therefore has much higher variation in levels of CO2 than the southern hemisphere. While variation still occurs in the south pole as a result of CO2 mixing with the entire atmosphere, the variation throughout the course of a year isn't as dramatic since there are no plants in the south pole.
In the year 1958 a man named Charles Keeling began measuring the amount of CO2 in the atmosphere at the Mauna Loa Observatory in Hawaii. Initial measurements showed that CO2 levels varied throughout the year as predicted, with highs in the spring and lows in the fall. As CO2 continued to be measured, the data showed that while levels varied throughout the year, the overall average of CO2 in the atmosphere was increasing annually. The lows each successive year were higher than the year previous, and the highs each successive year were also higher than the year previous.
The graph generated from this data is called the Keeling curve. It is the longest continuous measurement of CO2 on record, and it is often referenced as proof that CO2 levels are increasing due to anthropogenic sources of carbon.
Although the measurements from the Mauna Loa Observatory are the longest continuous measurements of CO2, ice cores can give us data about levels of CO2 in the past. Looking at bubbles in the ice, we can measure air from the past and extrapolate overall CO2 levels. Depth and location of the ice tell us how old the air is. The further back in time we go the less reliable the data is, but we have data from the last 500,000 years that is fairly accurate.
This video shows measurements at Mauna Loa vs the South Pole forward through time in order to build a Keeling Curve, then goes backwards through time to show ice core data. Large dips in CO2 levels are a result of Ice Ages, while little dips are thought to be natural variations. The extreme increase beginning in the year 1800 correlates to the Industrial Revolution, when we began burning large amounts of coal and oil for power.
Looking at a graph of global temperatures and graphs of CO2, one can see that the overall increase in temperatures correlates to an overall increase in CO2.