A new generation is when a new game includes the following.
Is not reverse compatible with previous games(Meaning the previous games can trade to it but it can not trade back).
Example: Gold and Silver were the start of Gen II which had new Pokemon, it was the new Johto region, and while you could send Pokemon from R/B/Y to it you could not send them back.
However in Gen IV there was Heartgold and Soul Silver, this was not the same region as the other Gen IV games (Platinum, Diamond, and Pearl), but this was not a new region, it was a region from Gen II and it had old Pokemon and it could trade directly with the other Gen IV games.
Gen I: Red, Blue, Yellow, Green(Japan); Region: Kanto
Gen II: Gold, Silver, Crystal; Region: Johto
Gen III: Ruby, Sapphire, Emerald + Fire-red and Leaf-green; Regions: Hoenn + Kanto
Gen IV: Diamond, Pearl, Platinum + Heart-Gold and Soul-Silver; Regions: Sinnoh + Johto and Kanto
Gen V: Black, White, Black 2, White 2; Region: Unova