An Inside View on a topic involves making predictions based on your understanding of the details of the process. An Outside View involves ignoring these details and using an estimate based on a class of roughly similar previous cases (alternatively, this is called reference class forecasting).
For example, someone working on a project may estimate that they can reasonably get 20% of it done per day, so they will get it done in five days (inside view). Or they might consider that all of their previous projects were completed just before the deadline, so since the deadline for this project is in 30 days, that's when it will get done (outside view).
The terms were originally developed by Daniel Kahneman and Amos Tversky. An early use is in Timid Choices and Bold Forecasts: A Cognitive Perspective on Risk Taking (Kahneman & Lovallo, 1993) and the terms were popularised in Thinking, Fast and Slow (Kahneman, 2011; relevant excerpt)....