What does it mean that my baby would rather spend time with his dad?

Dad is important: It means that dad is involved and around. Sometimes competitive juices flow, and mom's take it personally when dad is the favored one, when usually mom is. There can be family dynamic that allows dad to be more of a presence, do more feeding, etc. Also, the baby may just prefer dad's smell, look and sound. The short answer is, don't sweat it. In time, you both will be very important.

Nothing: Does dad work outside of the house? Do you spend all day with the baby? Then the baby is excited to see a new figure when it walks through the door because it is "new and exciting" whereas you are the "same old and standard" the baby is used to on a regular basis. Give it time and it will even out. Don't read into something that isn't even there.