When a ham talks about "tone," it is generally a reference to subaudible tones. These are transmitted in the audio signal, but at low audio frequencies around 100 or 200 Hertz (the lower the frequency, the less likely to bother listening hams).
Tones go by several names - CTCSS (Continuous Tone Coded Squelch Systemn), the generic name; PL (Private Line), the trademarked name of Motorola's tone system for business radios; QC (Quiet Channel), RCA's name for it; and CG (Channel Guard), General Electric's name for it. They are all the same idea - a subaudible tone transmitted with the voice.
Why would anyone do such a thing? The answer is to differentiate between different users of the same frequency. The most common use for subaudible tones in amateur radio is for repeater access. A repeater will only allow a signal that includes the tone to be transmitted by that repeater. Therefore, random, noisy signals won't activate the repeater; neither will users of a distant repeater on the same frequency but with a different tone. "Open" repeaters (open to use by any ham) usually use tone just to keep out noise. "Closed" repeaters can limit repeater use to certain members by only letting members know the correct tone. The amateur operator is the one encoding the tone into the transmission.
On the other hand, the operator might decode a tone, too. In this case, the repeater encodes a tone; then whoever wants to receive the signal from this repeater - and not a signal from other repeaters - can set up "tone squelch" to ignore the frequency unless the receiver hears that tone. This "tone decoding" can also be used between multiple users of one simplex frequency, and as long as no one transmits at exactly the same time, separate parties can each use the frequency without bothering other parties.
Hint - if you have trouble transmitting into a repeater, and you're sure you ought to be able to, check your tone encode/decode settings. If you think you're encoding and decoding, try just encoding. This author has made the mistake of assuming that his radio can do both at the same time with different tones, when in fact it is an either encode/or decode/not both on his radio.