There is no such thing as the transcription of a word.
Strictly speaking, you can only transcribe a single utterance -- for example, how Kevin Russell pronounced the word cat at 12:58:03 pm on February 4, 2004. You can transcribe this utterance as exactly as possible, within the limits of your hearing and the conventions provided by the IPA.
If you want to go beyond that, to try to describe how Kevin Russell pronounces the word in general, or further still to how English speakers pronounce it in general, then you have to start making abstractions -- you have to decide which details to include and which to ignore.
It's common to distinguish between two kinds of transcription, based on how many details the transcribers decide to ignore:
The key factor in a broad transcription is meaning -- if a pronunciation detail can change the meaning of words in a language, it must be included in a broad transcription of that language.
For example, consider the difference between the vowels in [liv] and [lɪv].
With the symbols covered in this section, we are able to make broad transcriptions of Canadian English.
Some frequently asked questions about broad and narrow transcription.