I've read bits and pieces about Morgan and watched him captain numerous times, as I am sure we all have, but big things that stick out for me :
Clear head in pressure situations.
Presents himself as unflappable rather than manic, limited movement on the pitch and trusts his bowlers to execute.
Stern and disciplined - very rarely see anything off the field from him.
Experienced - both in terms of intl game and playing domestic around the world.
Uses data clinically and doesn't overload his team with it.
Big advocate of a style of cricket which suits England's strengths - fast, aggressive cricket.
The above probably allows for a bigger leeway of failings, as performances are almost always entertaining, and occasional failure is to be expected.
Respectful of opponents and teammates.
As you can see, I am a massive Morgan fan