What I mean by "appreciate".

ap·pre·ci·ate
/əˈprēSHēˌāt/
Verb

   1. Recognize the full worth of.
   2. Be grateful for (something).

   ^ see 1

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appreciate
  Use Appreciate in a sentence
ap·pre·ci·ate
[uh-pree-shee-eyt] verb, ap·pre·ci·at·ed, ap·pre·ci·at·ing.
verb (used with object)
1.
to be grateful or thankful for: They appreciated his thoughtfulness.
2.
to value or regard highly; place a high estimate on: to appreciate good wine.
3.
to be fully conscious of; be aware of; detect: to appreciate the dangers of a situation.
4.
to raise in value.
verb (used without object)
5.
to increase in value: Property values appreciated yearly.

^ see 3

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ap·precia·tory (-sh-tôr, -tr) adj.
Synonyms: appreciate, value, prize1, esteem, treasure, cherish
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).