The term mod is a very broad term and is used to describe many different things. It is short for modification, and is thus used to describe anything that is a modification of the default game. Additionally, game types are very often referred to as mods, even though some of them were always a part of the default game. The other most common use of the word is in reference to what the in-game server browser calls a rules set. In addition to these, some players will also occasionally refer to scripts and maps as mods, though it is widely accepted that that is an incorrect use of the term. All uses of the word "mod" on this site will be in reference to the "rules set".
One metaphor that may help clarify the word (if you need clarity), is to think of mods as completely different planets. Heck, you could even look at them as different universes. Mods can change any number of things about the workings of the game. Some mods add and subtract custom weapons, armors, packs, vehicles, etc. Others change the physics of the game along with many other small details. Pretty much anything can be changed by modding. One thing that is not determined by the mod, is the objective of the game. The objective is defined by the game type, not the mod.
When you start up a server, you first have to decide what mod you want the server to run. You then add the mod to the command line when you start up your server, and that's that. The game type and map can be changed at any time. In order to change the mod, you'd have to turn off the server and then restart it with a different mod.