DTC stands for Distributed Transaction Coordinator. DTC is the MS component that is used for distributed transactions, i.e. transaction queries that spans across different servers. A familiar recollection of DTC would be in queries that start with the BEGIN DISTRIBUTED TRANSACTION statement.
MSDTC is responsible for governing the distributed transaction and following up with the two phase commit required. MSDTC would have to be installed on the computer that hosts the SQL instance that initiated the distributed transaction, otherwise the query would error out. A quick FAQ on MSDTC and SQL Server on a cluster in this link.
With Windows 2008 there is the option to use multiple DTCs which has to be mapped to each SQL server. More reading on this is here.