This model basically states that the number of species on an island is a balance between immigrants and a natural rate of extinction. Increase the rate of immigrants, and the number of species rises. Increase the rate of extinction, and the number falls. You should try to graph this. On your graph, the point where the immigration line and the extinction lines cross, that's your island avifauna.
Island birds are vulnerable to extinction. They must have large populations but they aren't good competitors: they're not specialized. For example, a Woodpecker Finch on the Galapagos makes a passing poor woodpecker, even though that's the "niche" the finch is using. (It collects a small twig to dig out insects from wood.)
Two factors that affect island avifaunas are: 1) distance: the further out an island is, the immigration rate becomes lower so fewer birds. SHOW THIS ON YOUR GRAPH. 2) size: extinction rates are larger on small islands, so small, distant islands will have really small avifaunas. SHOW THIS ON YOUR GRAPH. If this sounds real confusing, try Googling it.
This model has proven hard to prove in field but is useful in its predictive value.