Phonemic transcription is a system used for using letters or symbols to represent sounds in speech. It is arguably different from the better known phonetic transcription. Phonemic transcription gives less detail than phonetic transcription, and aims only to cover the information needed to avoid confusion.
The basis of phonetic and phonemic transcription is the phoneme. This is defined as the smallest part of a word's sound that can be clearly defined as a separate sound that could affect the meaning of what a person says. This can vary from language to language. For example, in English the difference between "d" and "t" in "dime" and "time" should be clearly distinguishable and is enough to change meaning. In some other languages the two sounds would be pronounced the same way, meaning the two words couldn't be distinguished.
Phonetic transcriptions attempt to represent sounds as letters and symbols, making it possible for people to know how a word is pronounced without hearing it. The most common place people will see a phonetic transcription is in dictionaries. Many transcriptions use a standardized set of symbols, which means it can be possible for people to read and understand the pronunciation of words regardless of the language they speak.
Such transcriptions are usually classified as broad or narrow. Put simply, the narrower a transcription, the more precisely the symbols represent the actual sound of the pronunciation. The drawback is that this usually requires more symbols, which both lengthens the transcription and decreases the number of people who can use the system because they know all the symbols. Phonemic transcription can either be classified as a very broad phonetic transcription, or as not a phonetic transcription at all. This is because it simply conveys the sound, and gives little or no additional information.
Specifically, phonemic transcription does not distinguish between allophones, which are two sounds that are technically different, but where this difference is not an issue for communication. For example, the "p" sounds in "penny" and "spend" are technically pronounced in a different way, and thus would usually be listed differently in phonetic transcription. If the two sounds were swapped round, the two words might sound slightly odd to a listener, but they would still be clear and neither would be confused with another word. This means they are allophones, and thus are both listed the same way in a phonemic transcription.