As an adjective すぎる means too much, as in よすぎる (yosugiru = too good) or おいしすぎる (oishisugiru = too delicious). In its verb form, 過ぎる (すぎます) means to go beyond.
From Jim Breen’s online WWWJDIC
過ぎる 【すぎる】 (v1,vi) to pass; to go beyond; to elapse; to exceed;