We hope for things that we don’t necessarily know if they are true, such as our own salvation.
4 For, for this intent have we written these things, that they may know that we knew of Christ, and we had a hope of his glory many hundred years before his coming; and not only we ourselves had a hope of his glory, but also all the holy prophets which were before us.
Hope is something that is obtained, and is as real as faith.
11 Wherefore, beloved brethren, be reconciled unto him through the atonement of Christ, his Only Begotten Son, and ye may obtain a resurrection, according to the power of the resurrection which is in Christ, and be presented as the first-fruits of Christ unto God, having faith, and obtained a good hope of glory in him before he manifesteth himself in the flesh.
How do we know we have obtained it? Jacob tells us:
6 Wherefore, we search the prophets, and we have many revelations and the spirit of prophecy; and having all these witnesses we obtain a hope, and our faith becometh unshaken, insomuch that we truly can command in the name of Jesus and the very trees obey us, or the mountains, or the waves of the sea.
Moroni explains all of this as well:
40 And again, my beloved brethren, I would speak unto you concerning hope. How is it that you can attain unto faith, save ye shall have hope?
41 And what is it that ye shall hope for? Behold I say unto you that ye shall have hope through the atonement of Christ and the power of his resurrection, to be raised unto life eternal, and this because of your faith in him according to the promise.
42 Wherefore, if a man have faith he must needs have hope; for without faith there cannot be any hope.
43 And again, behold I say unto you that he cannot have faith and hope, save he shall be meek, and lowly of heart.
What are some of the affects of having hope? Good works. (See also Ether 4:5)
19 And after ye have obtained a hope in Christ ye shall obtain riches, if ye seek them; and ye will seek them for the intent to do good—to clothe the naked, and to feed the hungry, and to liberate the captive, and administer relief to the sick and the afflicted.