Tone refers to a change of pitch on the tonic syllable of a tone group in an utterance. In English there are five tones, usually indicated by an arrow over the tonic syllable, or a diacritic in front of it :
So, eg, She was a bit de\pressed indicates falling tone on the syllable "pressed" (/prest/).
There have been many attempts to give a systematic account of the meaning of intonation, some writers associating specific tones with specific grammatical patterns (eg rising tone for yes-no questions; falling tone for Wh- questions) or with specific attitudes and emotions. For me, the most convincing account is that of Brazil, Coulthard and Johns (1980), who explain the choice of tone as being dependent on the role of the information in the discourse. In brief :
Falling tone indicates knowledge that is new to the discourse and the listener. Eg if I say I'm going to \London, I'm telling you something new. But if you then ask me when, I might reply I'm going to \/London after I've been to \Leeds.
In this last utterance London has become shared information - we both know about it already, and therefore has a fall-rise tone. The new information, with the falling tone, is now Leeds.
Their first distinction is therefore between new information (falling tone) and shared information (fall rise). However, new and shared information may also be queried - and this leads to a rise or rise fall tone respectively. Consider the following :
A : Is John still in /London?
B : /\London? I thought he was in \Leeds.
A introduces new information into the discourse (London) but queries it - rising tone. B repeats it with surprise - ie s/he is querying shared information - and uses a rise-fall tone.
To summarise, the basic distinction is between new or shared information, and stated or queried information :
new, stated - falling tone
new, queried - rising tone
shared, stated - fall rise tone
shared, queried - rise fall tone
Level tone is much less common in English than the other four tones, and often gives a sense of non-involvement or boredom with what is being said.
This is obviously a very brief, and therefore simplified, account of what is a very complex area. In particular, I've avoided the new terms that Brazil et al introduce for the different tones in favour of terms which will be more familiar to most teachers. However, as someone who can't always "hear" tone differences, I've found the framework extremely useful in the classroom in helping me work out why my learners' intonation sometimes seems wrong. If you're interested in the area, I highly recommend reading the book.
Brazil, D., Coulthard, M., and Johns, C. (1980) Discourse Intonation and Language Teaching, Longman
(Remember that Amazon often has used copies of the books you want at prices much lower than the advertised price. It's always worth checking out.)