Hi Kri,
although I don't have experience with IBM products, I think the IBM MQSeries is simply a messaging solution based on JMS where data between systems are exchanged via messages.
Typical ESBs take this one step further and offer a solution to connect many heterogeneous systems to
exchange data. JMS is only one possible transport protocol for well-know ESBs. There are many other protocol providers which can be used to connect applications to an ESB and "talk" to other applications via HTTP, XMPP, FTP, SMTP, JMS, TCP/IP and many more. All protocol components translate message data as needed to and from the common protocol which is used on the bus itself. The advantage is that no application has to care about the protocol other applications use as long as there's a component for its own protocol to connect it to the ESB.
Marco
p.s.: Of course this was only a very short summary of all the hype about ESB and SOA ;-)