1. To recognize the quality, significance, or magnitude of: appreciated their freedom.
2. To be fully aware of or sensitive to; realize: I appreciate your problems.
3. To be thankful or show gratitude for: I really appreciate your help.
4. To admire greatly; value.
5. To raise in value or price, especially over time.

Synonyms: These verbs mean to have a highly favorable opinion of someone or something. Appreciate applies especially to high regard based on critical assessment, comparison, and judgment: As immigrants, they appreciated their newfound freedom.
Value implies high regard for the importance or worth of the object: "In principle, the modern university values . . . the free exchange of ideas . . ." (Eloise Salholz).
Prize often suggests pride of possession: "the nonchalance prized by teen-agers" (Elaine Louie).
Esteem implies respect: "If he had never esteemed my opinion before, he would have thought highly of me then" (Jane Austen).
Treasure and cherish stress solicitous care and affectionate regard: We treasure our freedom. "They seek out the Salish Indian woman . . . to learn the traditions she cherishes" (Tamara Jones).