The meaning of "believe" in the Bible is pretty straightforward, but runs deeper than what appears on the surface. When in the Old Testament people were called on to believe in Jehovah, it meant a belief that Jehovah would lead them in spiritual things, not just natural ones, that following Him would lead to spiritual life. When people believed in Jesus in the New Testament, it meant believing in Him fully, as God Himself, all-powerful. Implied in this level of belief also was belief in what He taught and the importance to follow His precepts. That's why Peter sank while walking on the water; he began to see the human element of Jesus rather than God himself. It's also why Jesus could not do miracles in his home area; people there had known Him as a boy and young man, and could not believe in Him as God.

(References: Arcana Coelestia 6956, 6969, 6970, 7065, 8240, 8783, 10392; The Apocalypse Explained 815 [2-15])

813. Here is the patience and the faith of the saints, signifies that through these comes temptation, and afterwards the implantation of truth from good with those who are made spiritual by the Lord. This is evident from the signification of "the patience of the saints" (of which presently); also from the signification of "faith," as being the implantation of truth; also from the signification of "saints," as being those who are in truths from good from the Lord (See above, n. 204), thus those who are made spiritual by the Lord; for man is made spiritual by truths from good. "Faith" signifies the implantation of truth because faith with man is truth acknowledged in the heart; for unless it is acknowledged in the heart it cannot be one's own faith; and this is why "faith" is nowhere mentioned in the Old Testament, but "truth" instead; and indeed, the ancient people with whom was the church were wholly ignorant that faith was anything else than truth; and when they said that they believed in God they meant by it knowing and understanding truths, and willing and doing them, and this from the Lord. Thence it is clear that "faith" signifies the implantation of truth.

[2] "The patience of the saints" signifies the temptation of the faithful, or of those who are made spiritual by the Lord, because "patience" signifies spiritual patience, which is patience in sustaining temptations; and those have that patience who fight in themselves against the falsities that are contained in the dogma of faith alone and that adhere to it; for that faith is confirmed by reasonings from the natural man and from the Word wrongly applied and thus falsified. The temptations that such sustain when they fight against falsities are meant by "patience."

[3] "Patience" has a like signification in Luke:

Ye shall be delivered up by parents and brethren, and kinsfolk and friends; some of you shall they cause to be put to death; yea, ye shall be hated by all for My name's sake: in your patience possess ye your souls (Luke 21:16, 17, 19).

This is said of the last time of the church, when judgment takes place. The temptations that the faithful will then undergo on account of truths are described by "they shall be delivered up by fathers, brethren, kinsfolk, and friends, and be put to death," also "shall be hated for the sake of the Lord's name;" "parents, brethren, kinsfolk, and friends," meaning those who are of the same church, but who are in evils and falsities; their undergoing temptations is meant by "being delivered up to death" and "being hated;" therefore "in your patience possess ye your souls" signifies the preservation of the life of truth among falsities; "soul" signifying the life of truth.

[4] Again, in the same:

They who are sowed in the good land are those who in a simple and good heart hear the Word and hold fast, and bring forth fruit in patience (Luke 8:15).

"To bring forth fruit in patience" signifies to do truths and goods even when living amid falsities and evils, that is, among those who are in falsities and evils. The Lord's patience in temptations, of which He suffered the most grievous of all, is described in these words in Isaiah:

He endured persecution and He was afflicted, yet like a lamb He opened not His mouth (Isaiah 53:7).

"Enduring persecution" signifies temptations; "to be afflicted" signifies their grievousness; "to open not His mouth" signifies patience.