A postdoc (or "post-doc," "postdoctoral," or "postdoctoral research") fellowship is a training-focused position available to people who have earned a doctorate. Postdoc positions usually act as a stepping-stone between the student experience and the full-time professional experience. For the postdoc appointee, a postdoc position offers in-depth training. For the postdoc institution or organization, a postdoc is a dedicated researcher, with specialized knowledge but flexible to explore other topics, often with lower a financial cost than a permanent employee.
The most common type of postdoc position is a research-focused position at an academic institution, but postdocs also exist in industry, government, non-profit, and other non-academic organizations. Most postdocs are focused on research, but there are also opportunities in specialized areas such as technology transfer and policy at all types of organizations.
Academic postdocs tend to be focused on research and the academic experience. A postdoc typically has a higher degree of freedom in determining the direction of their research than a Ph.D. student. Postdocs are often expected to secure grants (as lead principal investigators or collaborators) and teach courses in addition to completing research objectives and publishing results.
Some research groups may offer high-performing Ph.D. students the opportunity to stay at the same institution, even within the same research group. Treat any offer like this carefully! It is an honor to be recognized as such a benefit to the research group, but will you be able to get the training you need if you stay in the same location? Also be aware that many future employers prefer candidates who have taken risks by moving to a new area (mentally, if not physically) and have broadened their area of expertise.
Industry postdocs can vary significantly between organizations. Most have a focus on teamwork, while valuing independent thought and development. A postdoc may be viewed as a "stepping stone" position, somewhere between an entry-level position and a higher-value research position... or it could be a distinguished staff scientist position with an opportunity for higher pay. For many organizations, while the postdoc position is a one to two year contract, it can serve as a pathway to a permanent position within the organization. Many industry postdocs offer easier access to state-of-the-art facilities, whereas many academic postdocs only provide access to these facilities through collaborations with other organizations.
Government postdocs have some similarities with academic and industry postdocs. Like academic positions, there is often an expectation to publish a high number of manuscripts; however, the salary offered may be higher than that of an academic postdoc. There may be fewer opportunities to write external grants, which could be a detriment to any future applications to an academic (especially tenure-track) position. Depending on the organization, there may be fewer opportunities to teach compared to an academic postdoc. Like industry postdocs, government postdocs can act as a stepping stone to a permanent position within the organization and can provide access to state-of-the-art federal facilities.
Non-profit postdocs can offer a less traditional option with similar benefits to academic postdocs. The focus of a non-profit postdoc can cover any topic, from food scarcity to sports management. There is likely a strong focus on grant writing and collaborative efforts, although possibly fewer opportunities to teach.