In phonetics, minimal pairs are pairs of words or phrases in a particular language, which differ in only one phoneme and have a distinct meaning. They are used to demonstrate that two phones constitute two separate phonemes in the language.

English "let" + "lit" proves that phones /e/ and /i/ do in fact represent distinct phonemes [e] and [i]. The phones do not have to be vowels, as the English minimal pair of "pat" + "bat" shows. In fact, this pair only differs in vocalization of the initial consonant as the configuration of the mouth is same for /p/ and /b/.

Examples

Following pairs prove existence of various distinct phonemes in English.
dime + time   /d/ and /t/
rot  + lot    /r/ and /l/
zeal + seal   /z/ and /s/
rhyme + time  /r/ and /t/ 
meal + meet   /l/ and /t/ 
feet + seat   /f/ and /s/

On the other hand, phones /p/ in "spin" and /ph/ in "pin" are both
allophones of the phoneme [p] and no minimal pair can be found to distinguish them. Languages like Cantonese distinguish between them and they represent distinct phonemes [p] and [ph].

Here is a minimal set in French:

cire   wax
sûre   sure
soeur  sister
sieur  sir
sueur  sweat
To an Anglophone, some or all of these sound alike, because the [ö] and [ü] sounds do not exist in English. A minimal triplet of consonants is
bête noire [betnwar] black beast, pet peeve
baie noire [benwar]  black berry (not blackberry, which is mûre)
baignoire  [beñwar]  bathtub
[tn] is not a single phoneme in French, so this shows a minimal pair between the presence and absence of [t] next to [n], which shares its point of articulation. [n] and [ñ] differ only in point of articulation.

There are three verbs in Hebrew which demonstrate the distinction, in some dialects, between a velar stop and an uvular stop on one hand, and a glottal stop with and without tightening of the throat on the other:

qara'  read, call
qara`  tear apart
kara`  kneel
In the following two hebrew verbs, the only distinction is a velar stop, in the middle of the first word:
lir'ot - to see
lirot - to shoot

In Korean, phones /r/ in Korea and /l/ in Seoul are allophones of the phoneme [l] and are perceived by native speakers of Korean as a single letter i.e. phoneme. The difference is that /r/ is pronounced before vowels.

In Spanish, /z/ and /s/ are both allophones of [s] and /z/ appears only before voiced consonants as in mismo /mizmo/. On the other hand, Spanish and Italian have many minimal pairs differing only in stress.

French and Latin have no distinctive stress, but Latin did have distinctive length of consonants (as does Italian) and distinctive length of vowels (as do German and Hungarian).

Languages such as Mandarin Chinese and Japanese, but also for instance Serbo-Croatian, Norwegian and Lithuanian have distinctive tone. (See: melodic accent and tonal language.)