To greet (someone) in a warm and friendly manner.
Used in somehow more formal register.
English equivalent: You're welcome.
There is no need to sign you since it is already understood in general contexts. When somebody says "thank you", you reply welcome in ASL.
Do not say your welcome in ASL. Understandably, it is common to see some English-speaking people saying "ur welcome" or "your welcome" in North America because it comes from the sound of you're welcome where it is the contraction of you are welcome. It might sound okay, if not strictly incorrect, in English, but it absolutely does not look right in ASL.