SPI_finish closes an existing connection to the Postgres backend. You should call this function after completing operations through the SPI manager.
You may get the error return SPI_ERROR_UNCONNECTED if SPI_finish is called without having a current valid connection. There is no fundamental problem with this; it means that nothing was done by the SPI manager.
SPI_finish must be called as a final step by a connected procedure or you may get unpredictable results! Note that you can safely skip the call to SPI_finish if you abort the transaction (via elog(ERROR)).