"Chief Rabbi" is a position which has no historical background within Judaism, although most countries have one (or more) nowdays.
The job of the Chief Rabbi isn't to be the "boss" of all the other Rabbis in the country - each Rabbi is usually employed by the Synagogue or organisation for which they directly work. His job is usually to represent the Jewish people of the country concerned to the government of the land, and also to make rulings on Halachah (Jewish law) that apply to the country.
Additionally, some Chief Rabbis become very respected people for more general matters. The former Chief Rabbi of Great Britain and the Commonwealth, Lord Immanuel Jakobovitz, was an expert on medical ethics and spoke in the House of Lords on this matter. Of course, his position was influenced by him being a religious Jew, but this wasn't the actual matter at hand.
Israel has three Chief Rabbis, which reflect three large groupings. One is primarily for the Ashkenazi population, one is for the Sephardi population, and one has special responsibility for the army, and the different religious decisions that need to be made.
The current Chief Rabbi of Great Britain is Sir Jonathan Sacks (having received his knighthood in the Queen's Birthday Honours list, June 2005.