to lay the foundation of something, and so to set it up firmly and make it last
The picture behind this word is a builder laying the first course of stone in the ground, the base on which everything else will stand. From that concrete image the word reaches in two directions. Used of an actual building, a city, or a wall, it names the literal act of laying a foundation, the unglamorous first step that decides whether the whole structure will hold.
Applied to God and the world, the same word says that He founded the earth, the mountains, and the heavens, setting them in place so firmly that they cannot be moved. Here the word is doing more than describing the start of creation; it is claiming that the world rests on a stable base that God himself put down.
From there it stretches once more to things that are not built at all. A king can found a rule, God can found his enduring promises, and a person can be appointed to a fixed office. In every case the same idea carries over: something is set down so deliberately and so solidly that it will stand. The senses below are shades of that one act, from stone in the ground to a decree that will not be revoked.