Distinctive brand assets are any images, shapes, colours, typefaces, sounds, words, phrases, characters or rituals that come to mind when people think about or come across the brand (and don't come to mind in association with competitor brands). Distinctive assets become connected with a brand in people’s minds if they are used across multiple touch points, consistently over time.
This short video explains the concept in more detail and how these assets benefit brands. This video goes on to talk about how to choose which assets a brand should focus on.
To hear about lots of great examples, check out this LinkedIn thread.
This (UK-centric) audio-branding quiz is designed to illustrate how sounds and music can connect a brand with long-lasting memories and strong feelings. This LinkedIn thread is about the same topic. See also this excellent video by Mark Ritson.