Fun fact: That's not Rika at the end of the series, that's Frederica Bernkastel, the witch who looks over the Higurashi world. Rather than try and write my own interpretation of her, I'm simply going to copy and paste what I read from Wikipedia since it's all the same.

Frederica is an omni-present being surrounding the Higurashi universe. Frederica is the writer of the poem about Rika's struggle to escape the fate of June 1983, giving hints about each arc. She likes playing with time and events, as seen in puzzle piece #52 and the end of the second season of the anime, entering an alternate world and stopping Miyoko's parents from dying. She even has an intention of making a world where Rika's or Satoko's parents did not die, or pairing Keiichi with various girls. Although she claims that she is not Rika, it's implied that she is the collective mentality of the several thousand reincarnations of Rika. The pronunciation of "Frederica" roughly resembles Rika's name in eastern order, and Bernkastel is well known for its wine. She is hinted to be one of the witches in Umineko no Naku Koro ni.

Of course pretty much all this information is found out in the Higurashi games.