See How Many Dots Has It Got for what is today still called VGA, but has evolved far beyond 640x480.
The resolution champion today seems to be WHUXGA (Wide Hex Ultra Extended Graphics Array) with resolution of 7680x4800 (36,864,000 total pixels).
Using VGA, the signal from the CPU is converted to VGA by the video adapter and sent to a monitor with VGA input. The conversion to VGA causes some loss of quality.
With DVI the signal is not converted (kept digital) and sent to the DVI input on the monitor.
DVI and HDMI are exactly the same as one another, image-quality-wise. The principal differences are that HDMI carries audio as well as video, and uses a different type of connector, but both use the same encoding scheme, and that's why a DVI source can be connected to an HDMI monitor, or vice versa, with a DVI/HDMI cable, with no intervening converter box.