Literally, "against the person." In personam refers to courts' power to adjudicate matters directed against a party, as distinguished from in-rem proceedings over disputed property.
A court with jurisdiction over a particular location may exercise in personam jursidiction over a person who resides, maintains connections, or is served notice of legal proceedings in that location. It may also exercise jurisdiction over a person who consents to be subject to it.
In personam judgments can be enforced against the person where she is, while disputes over property must take place in its particular location.