These verses are primarily about our relationship with God. Once you've experienced the power of the Word of God and become part of His family, this is how you are to respond to the Word in your life.
Quick to hear: if you're not paying attention it is hard to make progress.
Slow to speak: if you're quick to speak you may not be listening fully. This is not to say you shouldn't ask questions about the what is being taught - even Jesus did this. This could also be a warning against those with their own agenda (they may be focusing on their own priorities over God's). Some may also be eager to show how they are better are wiser than their teachers but they should remember the responsibilities teachers have.
Slow to anger: be careful about responding in anger - you may stop listening.
If God has saved you through the gospel, realize that you've come to Him as a sinner and He will accept you as you are. However, from that moment on He is going to want to address anything and everything in your life that is against Him and unclean. We honour the Lord when we listen to what He has to say and then obey Him.