From Wikipedia's Touchpoint Definition
A touchpoint can be defined as any way a consumer can interact with a
business, whether it be person-to-person, through a website, an app or
any form of communication (“Touchpoint Glossary”, n.d.). When
consumers come in contact with these touchpoints it gives them the
opportunity to compare their prior perceptions of the business and
form an opinion (Stein, & Ramaseshan, 2016).
and in context...
Touchpoints are an element in the IMC (integrated marketing
communications), which portray the willingness on behalf of the brand
communicators to use specific communication motives to reach the
appropriate target audience. This is used to engage customers in the
pre- and post-purchase experience when they purchase a good or
service. Touch points allow prospective customers to become
knowledgeable on the brand and the benefits offered and allow them to
make a decision to whether they will buy the product or service. An
example of a brand using effective touchpoints in their marketing
communications is Toyota selling the Yaris car model to the youth
segment. The way in which Toyota did this was firstly advertising the
Yaris in television programs such as Prison Break, whose viewers are
typically in the age bracket they were targeting. Toyota hosted an
Internet contest where consumers could create their own three-minute
television commercials. This method engaged the youth segment as it
was interactive and let the prospect consumers experience the brand.
Toyota also knew that the youth age group were social and would likely
attend social functions; this meant that Yaris cars were featured in
many sponsored events. They were also integrated into television
comedy programs, which attracted their target segmentation during
adverts.
These definitions and examples are very good to understand Touchpoints at a basic level, but of course there's a lot more to it, way more than what this site's format allows. See the Wikipedia link for example, it's really complete and thorough.
Outside of this, there are arguments for one-sided touchpoints (internal to the business), although I'm not so sure about that since I understand that you NEED a target audience that interacts with your marketing efforts, effectively creating connection nodes (or.... touchpoints!). Theoretically, they're valid, but again... IMHO those touchpoints are part of a different process