Three core senses: cover (verb, 盖被子 = cover with a quilt), lid (noun, 瓶盖 = bottle cap), and build (verb, 盖房子 = put up a house). The 'build' sense is colloquial; 建 or 建造 is the formal verb.
culture
盖章 — to stamp a seal — runs Chinese bureaucracy. A document without a red 公章 (official seal) is not considered valid, even if signed.
register
Rare surname reading 盖 also exists (Gě as a family name), but it appears in no common compound. In all everyday vocabulary 盖 takes the fourth tone.
Bottom 皿 is the indexing vessel radical — a low dish in profile with a foot-stand. The whole character pictures a lid placed over a container, hence 'cover, lid.' Same vessel family: 盆 basin, 盘 plate, 盐 salt-pot, 盗 steal.
Top is a stylized residue, not the sheep graph. The traditional 蓋 had 艹 grass over 盍 (lid-and-vessel); the 1956 simplification collapsed that upper portion into this 6-stroke shape that happens to resemble 羊. Read it as 'covering above.'
