The Arena file is a descriptive text included in the map .pk3 files. It is needed so that the map can be found in the "create server" and "map callvote" menus. The Arena file is not necessary for the map to function properly, but since it is simple to create and since it allows newbies to call a mapchange vote for it, not having an arena file is being frowned upon.
To make a proper arena file, just do what you always do when you have to conform to an established standard: Look how the others did it. This is the content of the arena file of the A.T.C.S. map:
{
map "atcs"
longname "A.T.C.S."
type "tremulous"
}
The first line contains the map name as it is known to the computer: It is the name of the .bsp map file (without the .bsp extension).
The second line defines the map name as it is to be shown in the above mentioned menus. Even though the key is called "longname", the name should not really be very long or it will be truncated. Color codes can be used even though their use is discouraged at the beginning of the map name because the Tremulous clients might fail at sorting those names alphabetically. This is of course a shortcoming that should be dealt with on the programmer side, so it's best to ignore that and hope that they will fix this bug since it's really child's play to strip unreadable characters from map or server names before sorting and displaying them, so it can be expected that this info is soon outdated.
The third line defines the game type which will always be "tremulous" for a Tremulous map. The software system used to create Tremulous and its maps is the "Quake 3" engine, just in case you wondered why there would be a game type descriptor key.
If your map name is "spacestation", then your .bsp file would be named "spacestation.bsp" and lie inside the .pk3 in the folder "maps", the arena file would be called "spacestation.arena" and lie inside the .pk3 in the folder "scripts". If the map name is "spacestation" but you are making release 003, then the bsp file would be named "spacestation_003.bsp" and the arena file would also be called "spacestation_003.arena".