According to Wiktionary, the word 游泳 is pronounced as /joʊ̯³⁵ jʊŋ²¹⁴⁻²¹⁽⁴⁾/. What exactly is the meaning of the numbers 214-21(4)? The first three numbers indicate the standard falling then rising pronunciation. What about 21(4)?
1 Answer
They represent tone height on a scale from 1-5, with one being the lowest and 5 the highest. Thus, a full third tone would be transcribed as 214 (starting quite low, falling, then rising up again), but since the final rise is optional, it's put in brackets. These are sometimes called Chao tone numerals, after 趙元任.
In the International Phonetic Alphabet, each number is replaced by a short bar at a certain height, then several of these are joined into a line that shows tone contour. So, the full third tone would be ˨+˩+˦=˨˩˦. Since this is sometimes hard to both type and display (depends on font), numbers might be easier.
Read more about tone representation with these symbols/numbers here: Tone Letter (Wikipedia)