Customers rarely buy after a single interaction. They might see a social ad, read a blog post from a search, click a retargeting ad and finally buy from an email. Multi-touch attribution is the practice of dividing the credit for that purchase across those touchpoints, so each channel's contribution is visible.
It contrasts with single-touch models such as first click and last click, which give 100% of the credit to one interaction. Multi-touch models include linear (equal credit), time decay (more credit to recent touches) and position based (most credit to the first and last touch). No model is objectively correct; each answers a slightly different question, which is why comparing them is so useful.