Here's a definition we copied for you: Horizontal Resolution
"Quality value of a displayed image relating the number of vertical lines of information (up and down lines) used to make up an image. Horizontal resolution measures the individual picture elements running along a screen from left to right."
"The greater the number of vertical lines (or picture elements running from left to right along the screen), the greater the resolution. Higher resolutions result in images which are better defined and more fully whole. With low resolutions, the individual elements of the image become visible but with higher resolutions these elements tend to blend together to form a solid, cohesive image."
Here's one for Vertical Resolution: Vertical Resolution
"Number of horizontal lines that can be output by a video display. Higher resolutions result in better quality pictures in which each individual line is more difficult to pick out from the complete image. Television resolution is often stated in vertical resolution. For instance, the resolution of a DVD is just over 500 lines."
Scan rates also determine overall picture quality. Here's a definition. Horizontal Scan Rate
"The number of horizontal lines of information a video display can paint onto a screen in one second given in hertz (Hz - cycles per second).
The horizontal scan rate of analog NTSC video is 15,750 Hz meaning that a video display paints 15,750 horizontal lines each second. By dividing this figure by the refresh rate (the vertical scan rate), the number of screens a video display can paint in one second, we can find the maximum number of horizontal lines a video display can produce (its vertical resolution). The standard refresh rate for video is 60 Hz (60 screens created per second). By this formula, a graphics projector with a horizontal scan rate of 63,000 Hz can produce up to 1,050 horizontal lines or a vertical resolution of 1,050. A data grade projector (31,500 Hz horizontal scan rate) can furnish 525 horizontal lines and a video projector or traditional television display (15,750 Hz horizontal scan rate) can furnish 262.5 horizontal lines.
The interlaced video format used by the analog NTSC television standard specifies that two fields create a full frame so that there are 30 frames per second. Each field thus contains 262.5 lines (each line spaced apart by one blank line; all the odd lines are drawn and then all the even lines are drawn in the next field to create a complete frame). When the two fields are combined, the NTSC standard allows for 525 horizontal lines of resolution (although only DVD approaches using those 525 lines with laserdisc using only 425, cable television around 300 and VHS tape just over 200).
The highest format of digital HDTV is interlaced featuring 1,080 horizontal lines. Thus every one sixtieth of a second, a field of 540 lines is created with two fields combining for a total of 1,080 lines in a frame. Graphics grade projectors can easily produce HDTV video as they can output 1,050 horizontal lines of resolution (when only 540 lines are created at a time). Data grade projectors will generally be able to show HDTV signals as well. Conventional televisions and video projectors are limited in their horizontal scan rate and cannot produce HDTV signals (they also are not digital in nature are still could not reproduce HDTV signals - data and graphics grade video projectors will need digital tuners to receive the HDTV signals)."
For "500 lines of horizontal resolution", this means if you inscribed a circle in the TV set, and displayed a pattern consisting of alternating white & black vertical lines, you could count 500 distinct lines across the diameter of the circle without the lines blurring together into a grey blob.