Maybe it's too obvious, but I'm not a native English speaker.
Basically it means you pay less money if you book the room weeks or months in advance. But note that such a rate usually means you have to pay a fee if you cancel or change the booking at any time, while paying the regular rate usually allows cancelling or changing the booking for free up to a day or two before.
As "the early bird catches the worm" you could book your hotel room way in advance and benefit from a cheaper rate here "early bird rate". The hotel also profits from that promotion rate if part of its rooms are booked ahead.