He used the apparent "resemblance" they have (they are both red heads) to crack jokes about her and how they are, in fact, long lost twins. Finland's citizens response was not what I had expected. As a matter of fact, it was the complete opposite of what I expected. It was a major factor in her winning the elections and even she acknowledged the fact that without him, she would not have won! She invited him to her country and had a date (more like a meeting) with him on valentine's day to show her appreciation.
Now that you know the background of the story, watch this hilarious video of Conan in an interview in a Finnish TV show. (Hint: Look at the male presentor pretending like he understands Conan's jokes)