What is the point of D0-D3 on LCD?

That type of LCD has two main modes of operation: 4-bit mode which uses 4 data pins (d4-d7), and 8-bit mode which uses all 8 data pins (d0-d7).

4-bit mode has the advantage of requiring fewer output pins on your Arduino. However, it means your sketch needs to send each command/character as two separate batches of 4-bits (one after the other). This is handled for you automatically by the LiquidCrystal library, so you won't need any extra complexity in your code. However, it does mean that your sketch requires roughly double the number of processor cycles to send anything to the LCD.

In contrast, 8-bit mode sends each command/character as a single batch of 8-bits. That simply means it technically runs a little faster.

With that said, a person looking at the display probably won't see a significant speed difference most of the time, as it still goes very quickly. The main impact will be on the microcontroller (the Arduino in this case). If it can use the faster 8-bit mode then it can devote a little more processing time to other things. That can be particularly helpful for timing-critical applications.

The answer is on the same page as the quote you mentioned (I have highlighted the important statement):

Creates a variable of type LiquidCrystal. The display can be controlled using 4 or 8 data lines. If the former, omit the pin numbers for d0 to d3 and leave those lines unconnected. The RW pin can be tied to ground instead of connected to a pin on the Arduino; if so, omit it from this function's parameters.

It turns out that the Hitachi HD44780 LCD display can work in 4-bit or 8-bit modes.