What does it mean when someone says I appreciate you?

[Angelbeliever1]

Yesterday I became a member of the church that I have been attending for 7-8 months. After the morning service someone shook my hand. While he shook my hand he told me I appreciate you. I've never had anyone tell me this. It was the first time that I heard someone tell me that. I know that I should know what it means. Thing is that no one ever told me that they appreciate me. So it is hard for me to understand. What does it mean when someone says I appreciate you?

[Anonymous]

TLDR:
I think most people use it to say 'thank you'.

Full version:
I use it quite a bit. For me, it is between 'acknowledgement' and 'thank you'.

Sometimes or in some situations, I don't think thank you is the right term to use. For me, thank you is more of a personal thing, i. e. if someone did something for me, then I will say thank you. At the same time, I think acknowledgement is a little to weak, as there is a level of 'gratitude' involved. Hence, the use of the word 'appreciate'.

[Anonymous]

It means that they appreciate having you in their lives.