Synesthesia is a neurological term meaning 'union of the senses', whereby sensations in one cognitive pathway can trigger activity in another. One of its most common forms is the perception of individual letters of the alphabet, numbers, days of the week or months as tinged or shaded with a certain colour, or as occupying precise places or orders on an imagined map.
In Nabokov's case, hearing a certain letter's name could result in an experience of colour, but of course his exposition here of "coloured hearing" is just another excuse for him to explore his love of words, and to show off his polyglottal knowledge. We do not know if Nabokov was any good as an artist, but he was taught drawing from an early age by Msistlav Dobuzhinsky, the celebrated Russian landscape painter of the time. Nabokov and Dobuzhinsky kept up a correspondence for decades later.
The now famous first lines of his scandalous novel of 1955 Lolita, "Lolita, light of my life, fire of my loins. My sin, my soul. Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta" is a good example of how much he enjoyed words and their sounds.
Other references to synaesthesia in Nabokov's work include the character Krug's description of the word 'loyalty' as being like golden fork lying in the sun in Bend Sinister.
Further reading: Nabokov and the Art of Painting by Gerard de Vries and D. Barton Johnson, in which the writers explore the rich presence of colour and painting in Nabokov's works.