Satire is the use of irony, humor and sarcasm to criticize something. Allegory is the hidden or symbolic meaning of things within a story. Dante has made use of these various literary tools in the Divine Comedy, in which he travels through the levels of the underworld, heaven and hell.
The entire journey of Dante is actually symbolic of the spiritual journey that man takes in search of God and self-realization.
The satire in this work is that Dante represents the story in a humorous way but in reality, it's a daunting, fear-inducing experience to visit places like the purgatory and hell and meet people who are being punished for their sins. So the fact that Dante is describing everything with humor instead of tragedy is satire. It's ironic. In fact, writing a comedy ( a work with a happy ending) on a serious subject such as hell or politics was really an unknown concept at the time and Dante's Divine Comedy was a very unique work for this reason.
Here are a few examples of satire and symbolism in the work:
The lion, wolf and leopard may be symbolic for several different ideas. Foremost, this is an idea mentioned in the Bible in which a lion, wolf and leopard play a role in the punishment of those who transgress. These may also be symbolic for the three types of sins.
Another one is the hill where climbing a hill has the hidden meaning of struggling to transcend ourselves and opening our mind and horizons to new things. The dark woods represent sin.
One satire is the punishment given to fortune tellers. Their heads are turned backwards, so if they walk straight, they cannot see where they are going. This is satire for what fortune tellers try to do. They try to "see" the future and tell it to others even though no one other than the Creator knows the future. So in an ironic way, they are punished to prevent them from even seeing where they are going when they walk.
There are also satires for Italian politics at the time.