Crests and Digieggs are used to equally strengthen your Digimon and each Crest and Digiegg has other effects.
Crest reinforce the status of all the Digimon in percent, for example Strength +1% and Digieggs increase the status in fixed values such as Strength +10.
To produce one of the two things you need that, what the Digimon often drop after losing a battle, so-called Drops. Here is a table just so you know what you need for which Crest or Digiegg:
 Friendship |

2x Floramon |

10x Gomamon |

12x Tokomon |
Attacke + 1% |

Hope |

2x Palmon |

6x Penmon |

15x Yuramon |
Abwehr + 1% |

Love |

3x Elecmon |

2x Mushroomon |

10x Motimon |
HP + 5% |
 Sincerety |

6x Koromon |

2x Gabumon |

6x Elecmon |
VP + 5% |

Light |

2x Tentomon |

4x Elecmon |

8x Yokomon |
Speed + 1% |
 Courage (Brave)
|

1x Friendship |

1x Hope |

1x Light |
Attacke + 1%
Abwehr + 1%
Speed + 1% |

Knowledge |

1x Friendship |

1x Love |

1x Light |
Attacke + 1%
HP + 5%
Speed + 1% |

Reliability |

1x Sincerety |

1x Hope |

1x Light |
Abwehr + 1%
VP + 5%
Speed + 1% |

Courage |

12x Vilemon |

15x Patamon |

25x Bukamon |
Stärke + 1
Agilität + 1 |

Friendship |

6x Biyomon |

12x Tsunomon |

2x Ikkakumon |
Vitalität + 1 |

Reliability |

12x Monzaemon |

12x Leomon |

15x DemiDevimon |
Stärke + 1
Vitalität + 1 |

Knowledge |

3x Kunemon |

2x Ikkakumon |

6x Pagumon |
Geschick+ 1 |

Hope |

8x Agumon |

2x Ikkakumon |

8x Salamon |
Vitalität + 1 |

Kindness |

15x Hagurumon |

15x Nyaromon |

10x Kabuterimon |
Stärke + 1
Geschick+ 1 |

Fate |

8x Kabuterimon |

12x Goblinmon |

15x Metalkoromon |
Agilität + 1
Geschick + 1 |

Wonder |

1x Friendship |

1x Reliability |
Stärke + 1
Agilität + 1
Vitalität + 1 |

Light |

1x Courage |

1x Knowledge |
Stärke + 1
Agilität + 1
Geschick + 1 |

Love |

1x Kindness |

1x Hope |
Stärke + 1
Vitalität + 1
Geschick + 1 |

Sincerety |

1x Fate |

1x Hope |
Vitalität + 1
Agilität + 1
Geschick + 1 |
If all the drops for a Crest or Digiegg are collected get a Teleportation Card (you get in an item shop) and head to the desert and there to Mud Village. Usually you should land there in the center of hot debates among many players who act together. And then you go first here:
There is the NPC Babamon and beside him Jijimon is standing. Speak to Babamon and you get several choices.
If you choose one of the first two options ( "Making a Crest/Digiegg" or "Merge several Crests/Digieggs"), a list of possible Crests and Digieggs that you can mix together will appear. If you choose the third option you can merge same Crests or Digieggs so they have a stronger effect.
Option 1: Making Crests/Digieggs with collected Drops
Option 2: Merge different Crests/Digieggs together
Option 3: Combine two of the same Crests/Digieggs
The first two options are explaining itself so we take a closer look to the third one. For many things, such as trade or even for yourself, you need this option. For example, someone wants you to give him a Brave +4 in exchange for clothes. But how to obtain these special Braves?
At the beginning you have a Crest or Digiegg on the level +1. When combining the same two things they increase the level by 1 for each merging. So the combination of two equal Crests +1, you get the same Crest on the Level +2. And so on ...
[+1] + [+1] = [+2]
[+2] + [+2] = [+3]
[+3] + [+3] = [+4]
Up to level +4 you can fuse Crests and Digieggs together with nothing more than the Crest or Digiegg, but to then go forward, we need a Booster, the in-game bosses often lose. But it takes some time already if you get to level +4. You can also buy this boosters from other players but they are very expensive. Anyway... Then it follows:
[+4] + [+4] + [Booster] = [+5]
[+5] + [+5] + [Booster] = [+6]
[+6] + [+6] + [Booster] = [+7]
and so on ...
From Level +7 then you need an additional object: The Fortune Digimon. Either one is going out for the forever-long mission to find it or buy it from other players, too and also for very high prices.
If you want to equip your Crests/Digieggs then you have to go to your Tamer status or you simply press the T-key on the keyboard. The first row from the top is provided for the Crests and the second one for the Digieggs. Overall, three Crests and three Digieggs are the maximum to hold.