frequency band and Bandwidth
As I understood, if the frequency range from 1 kHz to 3 kHz, does that mean that we have a signal that maybe repeat itself from 1000 times to 3000 time every second? 


No.

A signal can be composed of many different repeating signals that are added up. So, if you have a sine that repeats 1000 times in a second, and a sine that repeats 3000 times in a second, and you add these two up, you get a signal with energy at 1000 Hz and 3000 Hz.

But not all signals are purely sinusoidal. Those have energy not only at discrete frequencies, but over a range of frequencies.

There's different definitions of it, but essentially, the bandwidth of a signal is the width of the frequency range in which the signal has energy.

The way your material looks, you'll pretty soon learn about the Fourier Transform and  what Power Spectral Density is. That explains the mathematical foundation of how signals can have a continuous distribution of energy over a range of frequencies instead of just at discrete (i.e. separate, countable) frequencies.