What is the symbol ≙ most commonly used for in a mathematical or math-related context?

The hat above the equals sign is an estimator. Originaly estimators are used on terms. For example:

$$\widehat{\theta}(X)$$

But it has appeared (sometimes) more convenient to use it with an equals sign, especially in statistics. It has transformed a substantive (θ is an estimator for . . .) into a verb.

x ≙ . . . then reads as x estimates . . .

You use it instead of a plain equals sign when you do not have a strict equality between the left term and the right expression. Statistically speaking, it symbolizes an estimation of an unobservable quantity.