In his prophecy in Isaiah 9:6-7, Isaiah gives four names for the coming Messiah that describe what His ministry would be about. Each of these names is significant. They talk about Jesus' ministry while He was on earth and the way He ministers to us till today.
Jesus performed many miracles during His time on earth. His power was undeniable, even though people tried to attribute it to other things. He was accused of doing things by the power of the devil, when that would not have made any sense. For Jesus to do what He did while He was on earth, He would have to be a mighty God.
1. having, characterized by, or showing superior power or strength
2. of great size
3. great in amount, extent, degree, or importance; exceptional
If those are definitions of the word mighty, I would say they all apply when we're speaking of Jesus.
A mighty God can step in and act on our behalf for our good: Jesus came to do that for us. He was coming to as the Messiah to restore relationship with God and that meant He would step in on behalf of His people - both then and now.