The D-Rive (pronounced 'like 'derive', not 'drive') is the primary digivice used by the tamers of Digimon re:CONNECT.

Its primary purpose is to serve as a conduit for digivolution. It absorbs and stores data from defeated digimon and reconfigures it to be usable by the digimon linked to the device. The D-Rive is able to absorb data much more efficiently than a Digimon's natural processes can, especially when the data cloud is thinned by the effects of the real world, and this allows future digivolutions to happen much more easily (though it still takes practice on the part of the recipient digimon to maintain the higher form).
Each device is uniquely linked to both the digimon and the human they correspond to. Even though a D-Rive doesn't have to be actively operated to work (there's no 'hit button to Digivolve' button), it can't induce digivolution if it's not in close proximity to its human owner.

In addition to inducing digivolution, it includes a clock (accurate within a millionth of a second), a basic radar capable of detecting sources of digital energy in the real world (read: Digimon), the capability to 'store' its linked Digimon for transport (dubbed 'minmizing'), a Digimon database that brings up very basic info on digimon that enter its range, and a USB-compatible port.
The first time an unfamiliar digimon enters its range while the D-Rive is located in the real world, it will light up; after the first time, it will still bring up an entry on the radar, but won't independently activate.

When connected to a computer by its USB port, the D-Rive dumps a file that is both cryptic and heavily encrypted.

Digimon naturally have six stages of evolution, seven if you want to really split hairs:

Natural digivolution happens naturally throughout a digimon's life; even if it's stranded in the real world, as long as a digimon is in an environment where it has access to electronic communications, it will passively gain enough data to permanently digivolve naturally, though it takes many years.
(To wit, it took the digimon in the story about fourteen years to passively gather the energy to digivolve from in-training to rookie.)
Many digimon do not naturally grow past the Champion or Ultimate stages, though Megas are not unheard of. Theoretically any digimon could, with enough time, reach mega as their default stage, but the power and energy requirements are frequently astronomical.

Temporary digivolution done through the use of a D-Rive is generally refered to as an induced digivolution (or evolution). Unlike natural digivolution, which is permanent, induced digivolutions are temporary. As a recipient digimon becomes more adept at handling their power, induced digivolution can be maintained longer and done more easily.

Though they will still feel the effects and pain will linger, permanent damage tends not to be accumulated while in an induced higher stage of digivolution; a torn-off ear in champion form will not be sustained when the digimon reverts to their default form, nor will it reappear when the digimon next returns to that stage.

Drive Evolution, which elevates a digimon temporarily from Rookie to Champion using a burst of energy from the D-Rive, is a fairly straightforward process.
Initially, this is induced by either the digimon or their human partner being in direct physical danger. With practice, the forms can be activated functionally at will, though both the willingness of the digimon in question and the physical proximity of the respective human seems to be required, and maintaining this form will still exhaust the digimon over time.

Conduction and Catalyst Evolution both elevate a digimon from the Champion to the Ultimate stage.
Conduction evolution is the 'complete' form of Champion-to-Ultimate digivolution, created through a powerful bond between partners in times of necessity.
Catalyst evolution is the result of that burst of energy delivered by the D-Rive being "filtered" by the latent corruption carried by their paired digimon. It results in an extremely difficult to control and feral ultimate stage.