What is the use of the unused Data pins of a LCD
It has 8 data pins. The 8-bit mode is the standard mode, because the data is 8-bit: the characters are ASCII, and the DDRAM addresses are also 7 bit wide. In 8-bit mode you write them in 1 instruction, in 4-bit mode you have to split a byte in 2 nibbles, shift one of them 4 bits to the right, and perform 2 write operations.  

8-bit mode is just more simple.

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The 4-bit mode is often used today to save I/O pins. When the HD44780 was released microprocessors were far more common than microcontrollers. Microprocessors have data and address buses, and since most microprocessors were at least 8-bit that was not a problem, pinning-wise. And 4-bit microprocessors used the 4-bit mode. The control signals like R/W were also available, and the register/data select was derived from an address decoder, so that the LCD became memory mapped.

Most of today's microcontrollers don't have an external databus, and access the LCD through I/O pins through which the databus and the control signals are emulated. Smaller microcontrollers often don't have I/O to spare, and for those the 4-bit mode is a good solution.