Opening the book…
An estimate is a cheap model that returns the answer's size and rough magnitude before you commit to exact machinery. Its value is that it is independent of the detailed calculation, so it acts as a check: two different roads to the same order of magnitude rarely agree by accident. An estimate also tells you whether a problem is worth solving precisely at all, and which terms will dominate once you do.
Strip the problem to one or two dominant effects, round every input to one significant figure, and compute in your head or on a line. Keep the answer as "a few times ten-to-the-something." When the full calculation returns, compare: agreement builds confidence, while a factor-of-1000 disagreement means a units slip or a dropped term, not a rounding difference. Estimate first precisely so the exact result has something to answer to.
Estimation fails where the answer hinges on a small difference of large numbers, or on a delicate cancellation, since rounding destroys exactly the information that matters. Chaotic and finely-tuned systems can also defy any single-figure guess.