What is SPI Interrupt (SPIE) in SPI control register?
SPIE or "SPI Interrupt Enable" is used to enable the interrupt.

(Assuming you are in Master mode) There are two ways of transferring data using SPI:

1.Polling: Here you write data in SPI's data register (SPDR) and then poll on the flag for SPI Transmission complete (SPIF). 

2.Interrupt based: In this case, when you enable Interrupt for SPI, you write data in SPDR. Controller will transmit the data and will raise an interrupt when transmission is completed.

A question may arise that why there is interrupt for transmission but not for the reception, I am tempted to answer but It would be better if you figure that out! :-)