What does this "appreciate" mean? Simply, it is 1, but doesn't it have any possibility of 2 or 3?
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.
mo1-41 ex)If you are like millions of people, you’re probably receiving Christmas cards from people you know. Do you find yourself smiling at dozens of Christmas cards? Probably not. People receive so many Christmas cards during a season when they have too little time to read and appreciate them. They hear from dozens of people, which makes it far less likely that they will take a moment to remember you and your message.
A word is well spoken when all of its possible meanings come together.
In your example, if people read and appreciate the cards they receive, they become fully aware of the friendly sentiments the cards convey (3), they value the cards highly (2), and they are grateful they have received them (1). Indeed, the more they consider the cards, the more the value they attach to the cards increases. (And that last sentence conveys the original meaning of "appreciate", namely to increase in price or value.)