I am reading about wireless networks basics. I found three terms I cannot find exact definition for: channel, frequency band, frequency.
Can anyone give exact definitions for them?
If you don't know what a frequency is, you need to read up on waves-in-general and radio waves. But the other two terms can be defined in terms of frequency; frequencies are the “natural” thing and everything else are things people invented on top of that.
A frequency band, or band, is a range of frequencies with a specific least frequency and greatest frequency. Generally bands are used to describe some relevant range:
Channel has two different meanings:
Usage of a band can be channelized, which means that the radios which transmit on it do not pick frequencies arbitrarily but stick to a certain step size (e.g. 10 KHz for CB radio, so frequencies like 27.105, 27.115, 27.125 MHz). This makes it easier for a receiver to match a transmitter, and allows more efficient use overall as there are no wasted narrow gaps between signals. If you want to see a spectacular example of precise channelization, take a look at broadcast FM radio: stations with added HD Radio digital signals transmit right up to the limits of their channel.
In communications theory, the channel is the medium that carries the signal. This is a different kind of word than the others because it's an abstraction that is not about frequency, but it is like the above in that to look at an RF channel you ignore everything outside of the frequency range that defines the channel. Within that range, you care about the effects on the signal — loss, noise, multipath, fading, etc. — and those effects are frequency-dependent on a larger scale and possibly even within the channel.
A channel is a generally accepted stopping point - somewhere that we know other people or devices will be listening. For example, in the United States, amateurs get access to 5 distinct channels on the 5 MHz band. Or your WiFi router uses several channels, but most of those channels overlap.
A frequency band is a range of frequencies. They're usually referred to by the wavelength (e.g. 40 meters is the band from 7000 KHz to 7300 KHz).
A frequency is the reference point for tuning your transceiver. Depending on how you're communicating, you'll be using far more than that single frequency, but when people mention a frequency, that's what they're referring to - where you should set your transceiver.
For regulatory purposes, a frequency is usually used to refer to a carrier frequency, which has a specific meaning related to the mode of transmission (for example, in an SSB transmitter the carrier frequency is in theory never actually transmitted, but in a morse code CW transmitter it is the only frequency ever transmitted).
A frequency band is a range of frequencies with a lower and upper limit. If the regulations state that you must only transmit signals within a specified band, then you must make sure that your transmitted signals never go outside that range of frequencies - again, very easy to determine when transmitting CW, not so easy with SSB, AM or FM (requires knowledge of the bandwidth of the transmitted signal on each side of the carrier).
A 'channel' is an agreed-upon set of specific frequencies with additional information included in the agreement. For example, in the amateur 2m and 70cm bands, a portion of the band is 'channelised' and set aside for repeaters. These repeaters use specific spot frequencies for both their inputs and outputs, and have certain other requirements regarding mode (FM), deviation (for example, max. 3kHz) and other requirements for CTCSS tones and the like.
Even though this is an amateur "ham" radio forum, the OP's question seems to be about how these terms are used for wireless networks or maybe also in the field of telecommunication system engineering.
A channel has a more defined meaning in telecommunications and generally implied the use of specific modulation/demodulation schemes (e.g. FSK, PSK, etc.) and also specific management of control parameters and channel performance. This is all done to ensure quality communications.
Whole books in telecommunications engineering are written about channels and how to use them effectively for digital (usually) communications. Topics such as phase distortion, attenuation distortion, level control, channel capacity, equalization are all topics associated with channels in telecommunications engineering.
Alternatively, in ham radio, the use of the term channel is rare and about the only times I have heard it mention by someone it is referring to the US Citizens Band channels.
Frequency $f$ is the number of cycles that an RF electromagnetic wave undergoes per second.
Frequency band, sometimes denoted by $B$, is simply a range of frequencies (e.g. the band from 1-2 MHz).
Channel can be understood as "mini-band" within a band. For example, the CB radio band in the U.S. occupies 26.96 MHz to 27.41 MHz, with 40 distinct channels, allocated according to this chart by the FCC. Equipment manufactured for the CB service must provide discrete channels only according to the regulation. Wireless telephone services have similar channel allocations (though a cell phone user won't notice). Ham radio has no such channel restrictions.