What do "patterns, which separately match parts of a page" and "interactions between patterns" mean?
Simple patterns could mean regular expressions or extended regular expressions, each of which can be used to match parts of a page without considering the impact of other matches. 

Interactions between patterns could mean the conditional probabilities among all findings, either the matched patterns or the unmatched patterns. Additionally, they could mean more complicated probabilistic or logical rules.

We could dive a lot deeper and wider into the subject of information extraction. However, the understanding as basic as the above should be suffice for a first-time reading.