It is a voltage divider. Bluetooth is a 3.3v device so this arrangement cuts Mega's 5v Tx signal to 3.3v.
V to Bluetooth = V from Mega x R to ground / both Rs. = 5x2/3
Using a 1k would make it 2.5v, which is not enough.
About half the pictures you Google will show no divider. I have never heard of of anybody actually frying a Bluetooth because there was no divider, but there is no need for you to be the first.
You can safely ignore any other way of doing this that you might have seen and, just in case you want to ask, Mega has no trouble reading a 3.3v signal from Bluetooth. Note that there is nothing intrinsically wrong with that diagram from Mechatronics but IF you are using a tutorial from them, I suggest you do so very carefully, and best not at all.