Hope was a feeling of expectation and desire that something will happen in the future. The word could be used as a noun or as a verb. Hope was the expectation that nothing bad would happen. The opposite of hope was despair.
In 2067, the deep space probe Friendship 1 was launched by UESPA from Earth with the intention of finding alien species. Information within Friendship 1 was offered freely with the hope that one day Humans would stand on alien soil and extend their hands in friendship. (VOY: "Friendship One")
The Talosians placed their last hope in Captain Christopher Pike to save their species from eventual death as he had shown more adaptability than other specimens. However, this hope was not fulfilled as Humans were found to be unsuitable, preferring death over captivity and, thus, making them too dangerous and violent for the Talosians. (TOS: "The Cage")