Tags and crests were issued to the children during the first half of Adventure 01. The crest is a symbolic commodity which enables a chosen Digimon to digivolve into their Ultimate forms. This particular crest, the Crest of Hope, was discovered upon the entrance of Etemon's base of operation in episode 19, The Prisoner of the Pyramid. For this group of Chosen Children, the crests were assigned to each child based upon a trait they exhibited the day Greymon fought Parrotmon in Odaiba, 4 years prior to the adventures in the Digital World. Takeru's Crest, however, also wields power most of the others don't: through Angemon, Takeru's Crest of Hope gave Gabumon the ability to warp digivolve into MetalGarurumon. To do this, Angemon shot a surge of energy that came from Takeru's Crest into Yamato's back, causing the digivolution.
The crest also allows for Patamon's evolution into MagnaAngemon, a powerful Holy Angel Digimon that has shown superior powers against the faces of evil. "Hope" is the catalyst behind the powers of Patamon's evolutions, and it is later shown and proven that the crest itself isn't actually needed for this to happen: the power lies within Takeru's heart itself.