1. is very much appreciated, is very important
that person/gift/belonging means a lot to me
This expression is a way of indicating appreciation for something or someone. It is usually used to show that something has significantly affected you emotionally in a positive way. It is usually used in social situations to express gratitude or sentimentality. For example, if you were out sick from work for a time and your colleagues sent you flowers you could say, "Thank you, that meant a lot." It can be used in professional situations to express gratitude for positive feedback: "Thanks for noticing I put a lot of work into that presentation. It meant a lot." You can also use it to talk about objects that have significance to you or high personal value: "This necklace means a lot to me as it was handed down to me from my great-great-grandmother."