It's easiest to compare bandwidth to Plumbing. Bandwidth is basically how big the pipe is, which means if you have high bandwidth, you can usually have a lot of information going through the "pipe". If you have low bandwidth, think of having a narrow pipe (like a straw) which restricts the amount of information that can pass through at one time.
Amplifiers all have a gain bandwidth product that varies greatly from device to device. Obviously the bandwidth becomes important at very hi frequency. Is the gain enough for 100 megahertz for a gain of 10? if not you need another amplifier. also the bandwidth product is an indication of how close can one f/b without causing oscillations..
A carrier is used to make the wavelength smaller for practical transmission and to permit multiplexing. The spectrum is used to measure bandwidth (the range of frequencies) and the efficiency (the power in the side-bands compared to the total power) Bandwidth can be predicted using BW = 2 fm where fm = the maximum modulating frequency Efficiency depends only on the modulating index, m (the fraction of the carrier you modulate by) AM is limited to 33% efficiency because the modulation index cannot be increased to > 1.0 without introducing distortion in the receiver.
An analog multimeter measures values directly and is displayed using a meter. calibratin is done manually by adjusting the meter needle. A digital multimeter collects data at discrete times and the display is usually through LEDS. There is a bandwidh limit and calibration is often done with a click of a button which is much simpler compared to manually tuning the needle on an analog device