Digimon, Digivolution, & Virtues
Please not that nothing on this page -- except very obvious things! -- are meant to be taken as canon.

Digimon
A digimon-- as it is in every iteration of the Digimon franchise -- is a creature made up of data, capable of changing forms -- often radically, between forms -- as it learns and grows over time, accumulating data simply by aging.

In terms of Digimon re:GENESIS, a digimon has a 'baseline' level of data-- the data it has as a digitama that makes it an individual. This data takes the form of a Digicore. As a digimon gains more data, mostly simply by aging, it digivolves. The amount of data a digimon has is generally linked to its power (more data = more powerful), though there exist rare exceptions.
Most digimon have a handful of special attacks that they can perform; all of these use the data a digimon possesses. Whether it's spitting a fireball, creating a blast of light, casting a defensive spell, or simply enhancing a punch, all attacks are performed through use of a digimon's data. More powerful attacks, thus, use more data; however, even the most powerful attacks don't use a sizable fraction of their owner's data.

Data, like energy, cannot be created or destroyed; moreover, it is only truly lost by a digimon when they are forced to a lower form, and all 'lost' non-core data returns to Yggdrasil (see "Digivolution"). In most cases, a digimon's used data is restored fairly quickly with no adverse effects (IE, a digimon's attack spits a fireball; the fireball hits the enemy, disperses, and the data used by the attack returns, usually invisibly and unnoticed, to its owner), overexertion can force a digimon past the threshhold and force it to de-digivolve.

Special attacks are all paired with a name -- for example, Pummel Claw, Dragon Reaper, Pepper Breath, or Positron Laser -- and with very few exceptions, it seems that the attack name must actually be verbally called, like an incantation, for the attack to work. A digimon can perform simple physical attacks, such as a scratch, kick, headbutt, or bite -- without 'using' data, provided it has the anatomy required, but it rarely has a tremendous amount of effect.

Digivolution
When a digimon is defeated fully, in most circumstances, it reverts to a digitama, and all data not intrinsically linked to its Digicore is sent back into Yggdrasil for 'recycling'.
If a digimon's digicore is manually destroyed (which all but has to be done by a digimon, as no force of the digital world's nature has the power to do as such), the data will instead be absorbed by the digimon that destroyed it. This can be utilized the same as any other data-- if a Child-level were to, hypothetically, absorb a Perfect-level's digicore, they could immediately digivolve to Perfect. However, this is viewed as tantamount to heresy-- very, very few digimon are willing to do it, not even those under Era's commands.

The amount of data required to digivolve grows exponentially with the level; most digimon, over the course of their lives, reach Adult or Perfect level.

Note that Digimon re:GENESIS mostly uses the Japanese terms for digivolution levels, just because the author likes the way they sound. However, since "Ultimate" refers to a different level in Japanese than in English, to reduce confusion, it simply won't be used. Instead the two highest forms will be referred to as "Perfect" and "Mega".
To those unfamiliar, they correlate as such (listed Japanese -> English):

Virtues
Virtues are mysterious forces, embodied into talismans inserted in every Chosen Child's D-GEAR digivice. Through use of a Virtue, a temporary, accelerated digivolution can be achieved. A human owner of a Virtue is called a Virtue Holder; a digimon who digivolves through of a Virtue is called a Virtue Reciever. A partnership of a human and a digimon who utilize the power of a Virtue is, as a unit, called a Virtue Warrior.
(Note that this term, despite being singular, applies to the pair and only the pair-- for instance, the duo of Simon and Egakumon is called a Virtue Warrior, but neither of them is a Virtue Warrior alone.)

Virtue Digivolution
Virtue Digivolution is a form of accelerated digivolution, only possible through the partnership of a Virtue Holder and Reciever (a pair collectively called, as a unit, a Virtue Warrior). When a Holder's Virtue is activated, the virtue talisman borrows data and utilizes it in various ways, lending non-native data to the digimon and allowing it to temporarily 'jump' to a higher form.