You can think of a tone as a filter. If you have a tone set you'll only hear a station or repeater that transmits the same tone you have set. The only time a tone is required is when you want to use a repeater (or talk to another station) that requires a specific tone be sent for their radio to unmute. For that situation, you need to transmit a tone, but may or may not use a tone on receive. Be aware that at times a repeater may require a tone for it to retransmit your signal, but may not send a tone back. In that situation, you will need to set your station to only transmit a tone, but not require one to receive that repeater. A few repeaters may require one tone to transmit through the repeater and transmit a different tone back to you. Many radios will not properly handle this, but don't worry too much since there's an easy workaround, just program the needed tone on transmit and no tone on receive.
Most transceivers allow you to set no tone, a tone on transmit, or a tone on both transmit and receive. No tone will allow you to hear any station or repeater regardless of what tone they use or even if they don't use any tone at all. Setting a tone only on transmit will make it so you can be heard by a repeater or other station that requires that tone to be on for them to hear you. Setting a tone on both transmit and receive will allow a repeater (or station) that requires that tone to hear you and make it so you will only hear a repeater (or station) that's transmitting that tone. Often a radio will indicate what mode you have the tone set. If no tone is set (transmit or receive), it will show nothing in the tone area. If tone is set only on transmit, it'll show a "T" in the tone area. If a tone is set on both transmit and receive it'll show a "CT" in the tone area. Be aware that this is for CTCSS tones, there will be something similar for DCS tone settings, if those are set.
CTCSS and DCS are both analog styles of tones. CTCSS is a continuous tone that's generally too low for you to hear, but high enough for your radio to transmit and be received (some folks can hear a low hum when some of the higher tones are used). DCS or Digital Code Squelch, is a digital signal but sends a slow speed digital signal using similar tones to CTCSS in that they're too low for you to hear but high enough for your radio to send and receive. Don't be fooled by the word "Digital" in the name, it's designed for analog use. Digital signals have their own way of doing the same type of filtering.
CTCSS and DCS are the more generic terms for those types of tones. Some of the major companies may have their own terms that are simply their own way of saying the same thing. For example, Motorola calls CTCSS tones "PL" or "Private Line". They also call DCS tones "DPL" or "Digital Private Line".
