The Hertz is the SI unit of frequency (number of events per second), also known as "cycles [per second]".
In the video world it is primarily used to express three concepts, which conveniently use different multiples of the unit:
Pixel clock/Bandwidth (MHz)
When discussing graphics cards and other digital sources of video, the number measured in Megahertz typically refers to the pixel clock - how many pixels per second are output (including those wasted in blanking periods). A better video source, in this context, is generally the one with the widest range; minimum pixel clock limits are often the limitation in attempting to use a PC with a 15 KHz display.
If the topic is instead analog video processing, necessarily including at the very least the video final amplifiers used in a CRT display, the video bandwidth represents the performance of the related electronics: it is not strictly binding, as a monitor won't be damaged by supplying a video signal that exceeds its limit, but it will lead to a picture of insufficient quality (although often other factors limit sharpness earlier).
Cables also have a practical maximum bandwidth, affected by their length and quality, number and proper impedance matching of connections, etc; when using RF connections, the bandwitdh of the video channel (a subset of the television channel, defined by the lettered "system", ie "NTSC-M") is another constraining factor.
Horizontal frequency (kHz)
The number of lines drawn per second (including those wasted during vertical blanking).
This is, up to a point, the most important specification in a computer monitor, as it will determine the maximum supported "resolution" (once an aspect ratio is assumed); in fact, some of them only really support a single frequancy (within a modest tolerance), as is the case for certain workstation screens, the Apple eMac, and certain nonstandard industrial equipment displays. Newer devices will usually tolerate and reject an unacceptable signal but this cannot be deduced a priori, with some notoriously bad designs such as the IBM 5151.
It happens to be less of a concern with regard to SDTVs (and derived computer/industrial/professional monitors) only because the two video modes generally used in SDTV gear have very similar horizontal rates (15.734 kHz for 60 Hz NTSC, 15.625 kHz for 50 Hz), but yet again an obstacle is encountered here while attempting to use a TV as a PC display or vice versa, since not all GPUs support 15 kHz modes and most VGA monitors require a minimum of 30 kHz.
Contrary to common intuition a low frequency, if not stopped by the control electronics, tends to be more destructive than an excessive one: the horizontal deflection (a resonant system comprised of the final amplifier, flyback [more of an inductor than a traditional transformer], and deflection coil) fails to approach a short circuit only because of its large inductance, but that is exactly what will happen if a scanline takes too long to complete and the inductor has enough time to reach saturation. For this reason, a multiscan display often uses some mechanism to switch B+ voltages across various bands of supported frequencies, with lower ones being matched to lower voltages.
Vertical frequency (Hz)
The number of vertical retraces per second. Synonym: refresh rate.
Closely associated with frames per second, although the latter term may also refer to parts of the chain not strictly related with the properties of the video signal, and interlacing results in the Hz being a multiple of the fps (almost always 2x, even though higher interlaces are theoretically possible).
Tends to be more of interest in SDTV gear due to the two mentioned standards (not necessarily both implemented) and the existence of HD and/or scan doubling "100 Hz" TVs whose processing is undesirable for certain applications.
Newer multiscan computer monitors, on the other hand, tend to have ridiculously overkill maximum vertical refresh rates compared to typical subjective minimums for a stable picture, but might not be able to offer them at the highest "resolutions" due to both the amount of scanlines per frame and the vertical frequency increasing the demand for horizontal frequency.