it means a period of reflection or thought as you shared them.

When I heard about musing for the first time, I was kinda confused. It seems like having some sort of connecting with music. lol...

What I know the meaning of "Musing", I'm surprised. And it is really interesting.

Musing means think about something carefully and for a long time. It also means meditation or comment thoughtfully. 

I think that Musing is a catchy and awesome name for a question and answer platform. Hope this answers your question!

Musing means to meditate,ponder or think about something. Its more often is used define a time period of deep thought.

Eg. -
Somewhere in her musings she fell asleep.
Rama was lost in a personal musing as he looked out the window.
My musing about my lunch plans was interrupted by my clients knock on  the door. 

I'm not sure if you're looking for a definition of the word "musing", or if you are asking what the purpose of this very website is. I will answer the latter, since some people already answered the first one:

The meaning with musing.io is that people can ask questions to whatever they wonder about, and get a good answer. The people who write answers get paid cryptocurrency by participating, which incentivizes people to spend their time on writing good content.