An ELT Glossary : Aspiration

Put your hand in front of your mouth and say pin. As you say the /p/ you should feel a small puff of air hit your hand. This (the puff of air following the sound) is aspiration.

Now do the same thing, but say spin instead - and you'll feel no puff of air. The /p/ in pin is aspirated, while the /p/ in spin is not. However, whether the aspirated version of the phoneme is used in the word or the non-aspirated version, there's never any change in meaning - try saying spin but aspirate the /p/. It sounds a bit odd, but there's no chance of someone understanding a different word. The aspirated and non-aspirated versions of /p/ are therefore allophones of the same phoneme (ie variants that never cause a meaning change) rather than two different phonemes, and in phonemic script will both be written as /p/ - giving /pɪn/ and /spɪn/. This is always true of aspiration in English. In some languages, however, the difference in articulation does create a difference in meaning. In Korean, for example,  [p͈ul] means "horn",  while [pʰul]  means "grass". In Korean, these two sounds are therefore separate phonemes.

In phonology, which deals only with the sounds of a specific language,  allophonic variations are not taken into consideration of indicated in phonemic script, so "pin" and "spin" will be transcribed as /pɪn/ and /spɪn/ - as was said above. For phonetics however, which deals with speech sounds in general, irrespective of their use in specific languages, the difference in quality is important, and in phonetic script the aspirated variant will be indicated by the symbol [ʰ] - so [ pʰɪn] but [spɪn]

Related Reading

Kenworthy, Teaching English Pronunciation, Longman