In its purest definition, a model, or modelling, is the act of taking any past data and using that to make a prediction about the future.
"Betting Model" can mean several things. The one that Sando and Myself were referring to above is not anything to do with betting. A "model", is something that predicts...well, anything. Sports models are very common and there are limitless ways to create them and limitless things to predict within the sport.
Some common sports models predict things such as team totals, game score totals, winning margins, % chance of win, etc etc.
In its crudest form a model could be - looking at this data, the home team wins more than the away team, so I predict in the next game the home team will win.
More sophisticated models are obviously required to predict things such as winning margins and % chance of win. These take into account things such as HGA, recent performances, past performance against specific teams and at specific grounds, some models are even "player based" where they assign ratings to each player and use that to predict the outcome.
A relatively simple but successful team based model uses the following formula. Assign each team with a rating, and use that to predict the margin of the match, also taking a HGA into account.
Home team rating + HGA - Away team rating = Home team winning margin
note - How the teams are assigned ratings is quite complex and beyond the scope of this post, but in short an effective way of doing it is taking into account past results of the team with the most recent games being more "meaningful" to the rating (by using a function like exponential smoothing or a moving average).
2 examples.
1. Storm v Panthers in Melbourne
Storm Rated 6
Panthers rated 2
Storm HGA 4
6 + 4 - 2 = 8, therefore storm predicted to win by 8
2. Raiders v Roosters in Canberra
Raiders rating -4
Raiders HGA 6
Roosters rating 9
-4 + 6 - 9 = -7, therefore roosters predicted to win by 7.
Hope that all makes sense, have got a fair bit of experience in this area and happy to answer any further questions. Also That Guy, XYZ and TGM are all good people to talk to about modelling in general.