I am trying to understand the reputation of a journal in specific field of science. I am looking at this journal CHI Paper. How do I read the information from the graphs and figure out how this journal compares to other journals?
Look at the entire list of journals in the field Information theory, where this journals belongs. There you see that ACM Transactions on Computer-Human Interaction is at place 53 out of 248, ranked by AI. By combining this number with knowledge of the field you can probably draw some conclusions.
In general, both eigenfactors and the Article influence score (AI) are reported by Thomson ISI as well, so they are well known. Look at the FAQ at eigenfactor.org and read the wikipedia article on eigenfactor for more info. In general, AI is more comparable to the impact factor, while the eigenfactor scales with the number of papers published in the journal. Also have a look at SNIP and SJR if you are interested in journal metrics, info can be found at journalmetrics.com.