A non-rhotic speaker pronounces the r in red, torrid, watery (in each case the r is followed by a vowel) but not the written r of car, water, or hard. In most non-rhotic accents, if a word ending in written r is followed closely by another word beginning with a vowel the r is, however, sounded -- as in water ice. This phenomenon is referred to as "linking r". Many non-rhotic speakers also insert epenthetic rs between vowels (droring for drawing). This so-called "intrusive r" is frowned upon by those who use the non-rhotic Received Pronunciation but even they frequently "intrude" an epenthetic r at word boundaries, pronouncing, for example, Africa and Asia as Africa-r-and Asia.
For non-rhotic speakers, what was historically a vowel plus r is now usually realized as a long vowel. So car, hard, fur, born are phonetically [ka:], [ha:d], [f@:], [bO:n] (see SAMPA for a key to phonetic symbols). This length is retained in phrases, so car owner is [ka:r oUn@]. But a final schwa remains short, so water is [wO:t@]. For some speakers some long vowels alternate with a diphthong ending in schwa, so wear is [wE@] but wearing is [wE:riN]. Some pairs of words are homophonic for non-rhotic speakers but not for rhotic speakers; for example, spa and spar are pronounced identically by many non-rhotic speakers, but differently by rhotic speakers.
Areas with rhotic accents include Barbados, Canada, India, Ireland, and Scotland. In England, rhotic accents are found in Northumbria, the South West, and parts of Lancashire. Most of the northern and western United States is rhotic, except the New England region, and (for some speakers) New York.
Areas with non-rhotic accents include Africa, Australia, most of the Caribbean, most of England (especially Received Pronunciation speakers), New Zealand, South Africa, the southern United States (although pockets of rhotic speakers do exist in the southern United States, especially in northwest Alabama and middle Tennessee) and New England and New York, and Wales.
The case of New York is especially interesting because of a classic study in sociolinguistics by William Labov showing that the non-rhotic accent is associated with older and lower-class speakers, and is being replaced by the rhotic accent.
The word rhotic comes from the Greek letter rho, the equivalent of R.