This question came up in a conversation with a non-gamer recently and it reminded me of the chat I had with my "nearly gamer" work colleague.
The mainstream board game that is played by families across the world isn't that far removed from the hobby game scene. Sure the games are different but there are similarities with respect to how you play the games.
Now the first thing you have to consider is that these are games. In the mainstream market that usually translates into "competition" rather than anything else. It also usually doesn't include any real strategy elements other than perhaps in games like Risk which is one of those games that sits on the border between mainstream and hobby gaming.
In simple terms each game consists of the following -
Rules - These will vary based on format of the game and complexity level. Some hobby games are fairly light on rules whereas others will have pages upon pages of rules to govern the gameplay.
Chance & Strategy - I'm struggling to think of any hobby game that doesn't have a Chance or Random element to it. Almost all of them will involve some level of strategy though.
Rules in Hobby Games
These govern all sorts of things from how far you can move miniatures on a table, how cards interact with either other, how your player character does when trying to pick a lock etc etc. Different levels of rules and play styles will be covered by the rules of the game.
Chance & Strategy in Hobby Games
In most games this involves dice of some description. Whether that be the default 6 sided dice that you can find in most mainstream games but some games use different numbers of sides including but not limited to d4, d6, d8, d10, d12, d20 and d100.
For games without dice the chance element is normally managed through shuffling a pack of cards to ensure that the drawing of cards from the deck is relatively random.
So an example of this would be a wargame like Warhammer or Warmachine where the player elects to move their models by a pre-set (in the rules) distance and then opts to conduct an action that needs a random element (dice roll) to determine success.
In the main that's all there is to it - Action & Outcome. Sure you add things like story and for RPGs you also need to include the actual role playing but that's very specific and probably a post by itself