[This is a fast-access FAQ excerpt.]
A rhotic speaker is one who pronounces as a consonant postvocalic
"r", i.e. the "r" after a vowel in words like "world" /wV"rld/. A
nonrhotic speaker either does not pronounce the "r" at all /wV"ld/
or pronounces it as a schwa /wV"@ld/. British Received
Pronunciation (RP) and many other dialects of English are nonrhotic.
Many nonrhotic speakers (including RP speakers, but excluding
most nonrhotic speakers in the southern U.S.) use a "linking r":
they don't pronounce "r" in "for" by itself /fO:/, but they do
pronounce the first "r" in "for ever" /fO: 'rEv@/. Linking "r"
differs from French liaison in that the former happens in any
phonetically appropriate context, whereas the latter also needs
the right syntactic context.
A further development of "linking r" is "intrusive r".
Intrusive-r speakers, because the vowels in "law" (which they
pronounce the same as "lore") and "idea" (which they pronounce
to rhyme with "fear") are identical for them to vowels spelled
with "r", intrude an r in such phrases as "law [r]and order" and
"The idea [r]of it!" They do NOT intrude an [r] after vowels that
are never spelled with an "r". Some people blanch at intrusive r,
but most RP speakers now use it.