This term originally comes from psychology and a psychologist named Gibson, but it is now primarily used in design. Essentially, this is that “we perceive in order to act.” What we see shows us how to act based on its communication with us.
In early designs, affordances were very in-your-face, like the physical-looking ‘buttons’ in a Microsoft Word toolbar. Lately, though, they have been getting much subtler. This is a tradeoff between gaining aesthetics but losing usability and learnability of the design.
It might not be a huge deal for someone familiar with the context, but anyone picking up today’s mobile technology for the first time might have difficulty due to the subtle and inconsistently applied affordances popular in designs today.