Expansions are a big part of the hobby. For every board, card, role and war game that's published there's likely an expansion that goes along with it. Not a 100% situation obviously but it's likely counter-balanced by some games which have multiple expansions.
So what does an expansion bring to a game?
More of the same -
A lot of expansions take the base game and just say "have some more of that". That's fine and in a lot of games that's exactly what you want.
The majority of Settlers Of Catan expansions do little more than give you more.
Fluxx is another example. The core game is fine as it stands. The "expansions" for Fluxx are actually other editions of Fluxx but with a setting overlay onto the game. Zombie Fluxx is just Fluxx with Zombies. Does it change the game? Not really. Does it make the game better? Again not really. Does it make it more fun? Well if you like Zombies then it's likely going to add to your gaming experience but again the answer really is "not really".
Sentinels Of The Multiverse is sorta the same as Fluxx here as each expansion really only adds more Heroes, more Villains and more Environments. No real change to the game.
Yes there may be some new rules but those are only triggered as a result of that specific character etc.
Something different and new -
This is where the game has a new element that changes the style of play or more specifically how succeeding at the game occurs.
CCGs like Magic: The Gathering can have this experience multiple times a year through their "story" block sets and with each core set comes a new set of mechanics or indeed a new way of using existing mechanics.
Personally I feel this isn't really that different from "More of the same" above just it only involves a subtle change to how the game is played rather than the game you are playing.
Expands the game overall -
What do I mean by "expands the game overall"? Well I suppose I'm looking for are expansions to go further than those above. e.g. Gloom's expansions are sort of "more of the same" but with each expansion also adds an additional player to the game.
The Scoundrels Of Skullport expansion for Lords of Waterdeep goes a bit further as it adds a new player to the game and also brings a new mechanic into play too.
The biggest segment of tabletop games inside this category is RPGs. Yes a lot of RPG expansions can only be "more of the same" but a number of them add a lot of variations to the game being played.
Each of these are considerations on where that expansion sits on your "Do I buy this?" list.
I usually look for an expansion to be something that fits into the 3rd category as I want it to be more than a "rinse/repeat" exercise or a "we're going to mix it up a bit" exercise. If that's all an expansion will give me then unless I REALLY like that game I'm likely to skip the expansion and pick up another game entirely.