Middle English sille, from Old English syll "beam, threshold, large timber serving as a foundation of a wall," from Proto-Germanic *suljo (source also of Old Norse svill, Swedish syll, Danish syld "framework of a building," Middle Low German sull, Old High German swelli, German Schwelle "sill"), perhaps from PIE root *swel- (3) "post, board" (source also of Greek selma "beam").
The meaning "lower horizontal part of a window opening" is recorded from early 15c.; extended to the lower part of the case or frame of a door by 1590s. Used in geology in reference to certain types of rock beds or layers from 1794.