In answering this, we must first realize that not every freed slave would have had the same vision of freedom. Therefore, we can only generalize.
The general consensus is that freed slaves wanted two kinds of freedom above all. First, they wanted physical freedom. That is, they wanted the freedom to live where they wanted. They wanted the freedom from being beaten and/or sexually abused by their masters. They wanted the freedom to not worry about being sold or having their family members sold. In short, they wanted the basic human right of not being owned by someone else.
Second, the freed slaves wanted economic freedom. For most of them, the idea of being forced to work for someone else again was hard to stomach after having been enslaved. They wanted to have land and to have the means to work it. (Of course, it is doubtful that slaves who had worked in capacities other than that of field hand wanted “40 acres and a mule” but most slaves had worked in agriculture). This would allow them to truly be free because it would allow them to be their own boss.
Most freed people, then, wanted both economic and physical freedom.