Have you followed my recommendation in my answer to another question of yours to "read a tutorial on Principal Components Analysis by Lindsay I Smith, which is self-contained and easy to read"? Trust me, that is the fast way for you to learn and understand PCA. I might appear arrogant or opinionated. However, I want to emphasize you should follow my suggestion. That is probably the best help/answer you can get from asking all your recent questions.
Let me explain the quoted sentence a little bit. (It seems you are not familiar with linear algebra.) A linear combination of some eigenfaces means the sum of each of them multiplied by its corresponding coefficient. If this sum is the original image vector, we say the original image is represented by that linear combination. In particular, if we multiply all possible eigenfaces by its corresponding coefficient and then sum these weighted eigenfaces together, we will get exactly the original image vector, that is, we can exactly reconstruct the input image.
Why was "roughly" used in that article then? It was used only because we only have "20 eigenfaces that my training set generated". However, those are the most significant eigenfaces in the sense that their corresponding eigenvalues are the biggest 20. With only 20 eigenfaces, we can still reconstruct the input image but only "roughly". Another connotation of "roughly" comes from the fact that almost all numerical computations are approximations since, for example, we cannot expressed $\sqrt 2$ or even $1/3$ exactly in standard floating binary numbers.