The Mind-Brain Complex
There are lots of different understandings of the relationship between brain and mind, covering a spectrum of beliefs from the entirely mechanistic (it's all about the brain and there's no such thing as mind), to the entirely mystical (the mind is spiritual entity devoid of and unrelated to any physical properties). I might be wrong, but I'm going to explain how I see it.
Mind is an emergent property of a functioning brain. When a brain stops working, its mind disappears.
There are many metaphors which try to make the relationship between brain and mind easier to understand. I think of it as similar to the relationship between a crowd and its atmosphere.
A crowd consists of lots of different elements, just like a brain. Some work together, like two rival sets of fans chanting at a football match, and some are more individualistic, like the devotee who leaps on stage at a pop concert. All the joint and several elements of a crowd come together to create an atmosphere. The crowd is tangible and concrete. The atmosphere perceptible and abstract.
A feed-forward, feed-back relationship exists between the two. A fight breaks out in a crowd and the atmosphere becomes more tense, more threatening, and the crowd becomes more aggressive. And then life happens. A goal is scored, a band comes on stage, the sun comes out and the components of the crowd change, along with the atmosphere.
At the end of the event, the crowd disperses and the atmosphere ceases to exist.
The brain is the crowd, and the mind is the atmosphere. Both are complex, and interesting in their own ways.