The number in parentheses refers to section of the searched keyword/command.
As the manual is divided into several parts (user commands, system calls, C library functions, devices, file formats and various other topics), there is a need for a disambiguation mechanism.
By default, when you do not specify the section, it refers to section 1 (save some system configuration by determining another _default).
This is found in the "manual of the manual", and it being installed, can be accessed with:
man man
If we were to specify the section (we don’t need it, because command is default option) it would be:
man 1 man
The relevant part of the manual is this:
MANUAL SECTIONS
The standard sections of the manual include:
1 User Commands
2 System Calls
3 C Library Functions
4 Devices and Special Files
5 File Formats and Conventions
6 Games et. al.
7 Miscellanea
8 System Administration tools and Daemons
Note that this list can be extended by the authors of each distribution.
If you prefer, you can check this version online:
https://linux.die.net/man/1/man
Note that even in the online version, there is the section number before the topic.
Example of disambiguation:
https://linux.die.net/man/1/printf
https://linux.die.net/man/3/printf
That in command line would be:
man 1 printf
man 3 printf
In this case note that the first is the command of shell, and the second is from the library’s function C.
It is the "section" of the command.
– Bacco
No time to write an answer now, but basically: https://superuser.com/q/297702 and https://unix.stackexchange.com/q/3586
– hkotsubo