Resolution/Quality

When watching videos have you ever noticed how some videos are blurry and some are so crystal clear? That is a factor called "resolution". Resolution is the quality in which the video appears.
240p is a poor resolution it's rarely used anymore.
480p is a lot better
1080p is considered High Quality
Every so often you'll see resolution presented like "1920X1080" this represents that the resolution is being counted as Length/Width.

Equipment?

What type of equipment is necessary for professional looking videos?

Camera:
Inexpensive: A phone camera.
Average: Sony Cyber-shot DSC-HX400V - $400-$500
Expensive: Sony Alpha ILCE-7 - $1,698-$1,746

Camera Stands:

Sunpak - PlatinumPlus 5858D 58" Tripod

Any form of camera stands will generally work, however you may want a taller stand to be able to give your camera the flexibility to move in most any direction.