To be biased towards something means you favor it over something else. To be biased against something means you do not favor it over something else. So to be biased towards dogs means that you favor dogs over something else, such as cats.
Sometimes, people just say "I am biased" to mean they favor something. Below is an example of this:
My daughter is so talented, but I'm biased [=I am biased towards her].
I hope this helps.