The Godfests in Puzzle and Dragons are randomly occuring limited time events that enable players to pull at the Rare Egg Machine and get powerful monsters that can't be obtained via dungeons. The lineup usually includes the base forms of whatever pantheon (Hindu, Japanese, etc...) or some Evolved forms but at a lower drop rate. Godfests can cost 5-10 Magic Stones or the player can burn 25 magic stones for 5 pills.
New Player tips
For new players, it's recommended to do this sparingly as the drop rates can be poor for higher rarity monsters or the lineup just isn't worth it. Make sure you set a personal limit to how many times you pull so you don't lose all your Magic Stones.