The brown mailboxes if it's a USPS mailbox that is brown is a relay mailbox where the USPS workers can have access to more mail along their route.
This makes it so that the mail carriers don't have to return to the post office to get more mail as the brown mailboxes act as temporary storage for mail.
Also in most places the USPS has green mailboxes that are the relay mailboxes but the colors can vary from location to location.
Some people may also have brown mailboxes as well as residential mailboxes.
If you're referring to another type of mailbox that is brown it could also be the UPS mailbox which is also known as the UPS drop off box.
The UPS has drop off boxes for packages just like the USPS does for letters.
The mailbox should say what it's for and who it's owned by as well.