In English, for example, the phoneme /p/ has two allophones (note, the term allophone means other sound, from the Greek prefix allo- meaning other, and the word phone meaning sound). So, if /p/ has two allophones, it means it has two sounds.
Here are its two sounds, its allophones:
Aspirated, [pH], means a tiny puff of air is released as you pronounce, as in the word pit. Unaspirated, [p], means that a tiny puff of air isn't released at all, as in the word spit:
Test it! Hold a piece of paper up to your lips as you say pit. The paper should move because [pH] is aspirated. Now say spit (without pronouncing final [t]). The paper shouldn't move; [p] isn't aspirated; it doesn't have a tiny puff of air. In fact, that [p] almost sounds like [b]; spit ~ sbit;
The sounds (phones) [pH] and [p] are in complementary distribution: they never occur in the same place. Test it!
delete [s]: s[p]it => [pH]it (aspirated)
add [s]: [pH]it => s[p]it (unaspirated)
Delete [s] and [p] becomes [pH]; add [s] and [pH] becomes [p]. That's complementary distribution. [pH] and [p] never occur in the same environment. Switch the allophones, as shown below, and the result is a non-native pronunciation:
In short, allophones are different sounds of one and the same phoneme, and they never occur in the same environment. If you try to place them in the same environment, that is, if you pronounce spit as s[pH]it or pit as [p]it, it won't change the meaning of the word (that is, they are not distinctive like [p] and [b]), but the pronunciation will flag you as a non-native speaker, because allophones are the phonetics of a language: in English [p] and [pH] come from /p/. But that's just one language. In Chinese, however, [p] and [pH] are not allophones of /p/. They are distinctive. They can change the meaning of a word. In that language, /p/ and /pH/ are phonemes. It doesn't matter where they occur.
Other forms of allo-, allomorphs (morph: a minimal meaningful unit), as in the plural suffix -s:
The allomorph [s] occurs after voiceless sounds, and the allomorph [z] occurs after voiced sounds:
Allo-forms tell us that morphemes and phonemes can change pronunciation depending on their environment.