Why should I even care about the character of God?
Character is defined as an "essential feature; nature; the total of qualities making up an individual" (Webster). So the character of God is that which makes up who He is as God, and why He acts and speaks in certain ways. The character of God is who He is and what He is about.
Why should I care?
Understanding the character of a person is key to developing a relationship with him or her. So then, learning about God's character is the important part of knowing and serving Him. If you want to develop a strong relationship with God you must know what He is like!
Christians who don't understand the character of God are missing out on a universe of amazing things that one can discover about God. On the other hand, the less we know about God, the less we understand how He is working in our lives - so we get confused! The more you know Him, the more you trust Him. The more you trust Him, the easier it is to handle the difficult circumstances of life and grow in your relationship with Him - your Father and Creator.