What does it mean when "a gas is dilute in CO₂"?
In this case, it's comparing post-air-combustion $\ce{CO2}$ capture with pre-combustion capture, and with post oxy-combustion capture.

In the two latter cases, the  $\ce{CO2}$ stream is very highly concentrated.  However, with air-combustion, the flue gases contain a lot of nitrogen and NOx; hence the $\ce{CO2}$ is diluted in the flue gas, compared to the other two methods, where it's concentrated.

And as to Leonardo's supplementary question in the comments, about why the pre-combustion  stream has higher concentrations of $\ce{CO2}$ than the post-air combustion stream:

the comparison here isn't between two points in the same process. It's between analagous points in two completely different processes.

With post-combustion capture, the $\ce{CO2}$ is stripped out after the hydrocarbons (coal, gas, oil) have been burnt in air.

Whereas with pre-combustion capture, the hydrocarbon goes through a gasifier/shift process, resulting in a stream of $\ce{H2}$ mixed with $\ce{CO2}$. And at this point, the $\ce{CO2}$ is stripped out, and the $\ce{H2}$ is burnt.

And that's why the $\ce{CO2}$ concentration is higher in the pre-combustion capture process, than in the post air-combustion capture process.