DENISE is a contrived contraction of Display ENabler.

In the early days of the Amiga 1000 and Amiga 500, it was often called Daphne. There is no functional difference, aside from the revision used in early Amiga 1000s (8362 R5, typically a ceramic package) being unable to display the EHB graphic mode.

In the OCS and ECS machines, DENISE uses up to 6 bitplane data registers to get the display data that AGNUS (via its corresponding DMA channels) retrieves from chip RAM.

The bitplane data, in relation with the currently enabled graphics mode, result in a constant stream of 12-bit digital RGB output values (4 bits per Red, Green, Blue components) synced to the display mode. The digital data is then fed into a resistor network known as the Video Hybrid (or VIDIOT) which produces the final analogue RGB signal, still synced to the display mode, now ready for display on a TV screen or monitor.

DENISE also reads in (in multiplexed form) the axis information from both mouse ports.

It is also responsible for displaying any sprites being used, using up to 8 sprite data registers fed at the beginning of each scanline through Agnus’s corresponding sprite DMA channels BEFORE any bitplane data is read.

Furthermore, it handles the relative priorities between the display playfields and the sprites and can detect specific sprite/playfield collisions thus assisting in games design.

DENISE was replaced by the LISA Chip in the AGA Chipset (the only truly 32-bit component of the AGA chipset).

DENISE received a fully pin-compatible revision update, 8373 R4 (by default found in Amiga 3000, Amiga 500Plus, some late Amiga 2000s, Amiga 600) known as “Super DENISE” to differentiate it from the original chip.
Along with an ECS Agnus, it’s part of the ECS chipset.

These later versions of DENISE were capable of a greater range of screen display resolutions and scan rates, but also require an ECS Agnus (can be either a 1 MB of 2 MB version) to provide the necessary timings for the new display modes.
So it’s quite possible to “convert” any older A500/A2000 to ECS specs, the exceptions being the A1000 and the early “german” A2000, which use the “thin” 48-pin DIP Agnus variant instead of the “fat” 84-pin PLCC one. An ECS Denise can of course still be installed, but will behave as an OCS one.

The new display modes depart from the original NTSC/PAL-timed only modes (60/50 Hz, 15.7 KHz) and can use newer VGA-style displays, but since the default modes were still the original ones, this was practically only useful to owners of dual-scan or true multi-scan displays (such as the dual-scan Commodore 1940/1942 models).

Availability of such monitors had always been limited as only the ancient CGA and the already surpassed EGA modes used less than 31 KHz in the PC world. By 1991 VGA was the de facto standard and there wasn’t much reason for PC-oriented monitor manufacturers to support anything else.
This was partially solved with the availability of internal/external scandoublers/flickerfixers, which allowed the original modes to display on such monitors.

The Amiga 3000 models already came with a scandoubler/flickerfixer onboard. The same hardware (Amber chip based) was sold by Commodore as a separate video-slot card, the A2320 display enhancer, but as it supports 12-bit colour depth it was really suitable for the A2000 only.

A number of third-party scandoublers/flickerfixers for AGA-based Amigas were made, but some support 18-bit depth (262144 colours) instead of the full 24-bit (16777216 colours) AGA is capable of, and should be tested with a 256-level grayscale pattern to reveal such limitations (if relevant info is unknown or not clear enough).