Anchor text is the clickable text portion of an HTML link (<a> tag). In "<a href='...'>this text</a>," "this text" is the anchor text.
Anchor text is what tells both readers and search engines something about the page a link points to. Google's own guidance on links describes good anchor text as descriptive, reasonably concise, and relevant to the page it sits on as well as to the page it links to. A page linked with the anchor text "how to use shortened URLs" is treated as being about the topics "shortened URLs" and "how to use."
A commonly used breakdown sorts anchor text into exact match (the target keyword itself), partial match (a natural phrase containing the keyword), branded (site or company name), naked URL (https://example.com), generic ("click here," "learn more"), and image link (the image's alt text serves as anchor text). This grouping is a convention used for explanation, not a classification published by any search engine.
A key consideration with shortened URLs and anchor text: pasting a shortened URL as plain text makes the anchor text a meaningless string like "https://miji.be/abc123." From an SEO standpoint, even when using shortened URLs, wrapping them in an HTML link with meaningful anchor text is preferable. Where a link cannot be written as HTML at all, such as in messaging apps, SMS, or printed material, the notion of anchor text does not apply. In those places, spelling out the destination in the sentence around the shortened URL is what gives the recipient something to judge by.
The main pitfall in anchor text optimization is overusing the same keyword. Google's spam policies list optimized anchor text embedded in guest posts and press releases as an example of link spam, and state that sites violating those policies may rank lower or not appear in results at all. As a rule of thumb for what counts as too much, Google itself writes that if it feels like you are forcing keywords into the anchor text, it probably is too much, and suggests reading the anchor text on its own, out of context, to see whether it still makes sense. A natural link profile contains a balanced mix of branded, naked URL, generic, and keyword-containing anchor texts. Penguin, the system once known for tackling link spam, was announced in 2012 and folded into Google's core ranking systems in 2016, so it is no longer a separately named system.