Clinton called Palin after the election, when she was taking hits in the Alaska press over whether she really gave birth to her daughter, Adams reported toward the end of her column. The former Republican vice presidential nominee didn't believe it was really Clinton, having been famously fooled by that oh-so-clever Nicolas Sarkozy impersonator during the election. She refused the call at first, but then later her people vetted everything. Clinton presumably wanted to convey support for Palin having to deal with, uh, "false" rumors in the press about her personal life, since he knows how that goes. Or maybe he just wanted to, like, talk, catch up on things, whatever.
Since Palin is considered a sexy little firecracker, at least as far as potential Republican saviors go (sorry New Gingrich), and since Bill Clinton is basically known as an unreformed, greasy horndog, the gossip about the phone call could all be a ploy to embarrass Bill Clinton, and thus Hillary Clinton, and thus Barack Obama, by making it seem like the former president is constantly calling attractive lady politicians on any old pretext.
More likely the unsavory task of having a conversation with Sarah Palin was handed to Bill, by Hillary, as one of the many terrible chores he is constantly doing in return for having ruined her life in numerous ways, both personal and political.