The King is normally the person who won the Crown Tournament (there are rare cases where a female fighter has won), for the honor of their consort, who becomes the Queen (except as noted). The King and Queen are the ceremonial heads of the Kingdom.
Historical Note: The first time a King was named was at the First Coronation and Crown Tournament, March 25, 1967 (AS I, 1967). The first person so named was Henrik of Havn, who won the Crown Tournament in September of 1966, the crown was placed on his head by Fulk de Wyvern, who had won the previous tournament. Henrik and Wendryn were actually given scrolls at the tournament in September (1966) to commemorate the event, that named them King and Queen, but the titles weren't "official" until later.
A branch of the SCA with the ceremonial leaders King and Queen. The first Kingdom of the SCA was The West Kingdom, although when the SCA was started, the name used to refer to it was often simply "The Kingdom", if any name was used at all. When the East Kingdom was formed (June, AS III - 1968) and named "The Kingdom of the East", the "Kingdom of the West" became the "official" name of "The Kingdom".
A Knight is a peer of the realm, named so for his or her capability on the tournament field. A Knight is a member of the Order of Chivalry, which also includes Masters of Arms. A Knight is entitled to wear as regalia a chain of large open links (to signify his/her fealty to the Crown), a white belt (to signify his/her prowess) and a pair of spurs (to signify his/her rank). Note that a Knight must swear fealty to the Crown and Kingdom when they are made a Knight, a Master of Arms does not. A Knight is styled "Sir (Name)". There are a variety of Title Language Equivalents that can be used for those who wish to use a specific language for their persona.
Historical Note: The first Knight of the SCA was David the Herald, named so at the first tournament (May 1, 1966), by [Duke] Siegfried von Hoflichskeit. Note that members of the Order of Chivalry are equivalent in rank to the members of the Orders of the Laurel, the Pelican and the Order of the Rose.