Show don't tell is a writing technique mostly used in fiction or informal writing to better elaborate on a character or type of setting. You can nevertheless use the idea in formal or business writing such as in an email while still being concise.
More important for us Software Developers - is to put emphasis on the show part - and the way it drastically improves communication. We just ignore the details we would usually add with informal writing.
The philosophy behind is to show the proof and not only tell.
Consider this scenario:
You write a short memo to your supervisor stating what you've done:
Instance A - Telling
I've completed the task 2345, which is about sending an email to a customer when the latter has paid for an item.
Instance B - Showing
The same description as above - but you give an example and provide screenshots or a small video.
When Customer Bob logs into his account and selects item Coffee Mug X to buy, after making his payment, he should receive an email confirming his payment.
The second instance takes more time to prepare, yet is far more effective as a means of communication. There is less room for assumptions and has more description on the actual context - requiring thereby less guesswork for the recipient.