A pivot is the upper or lower boundary of a meaningful technical price range. It is basically a form of support and resistance where volume doesn't play a role. A pivot represents a key or pivotal price level that -when broken- has the power to show the path of least resistance. However, from a technical analysis perspective, such a pivot price level can also be represented by a sloping trend line.
I usually use the term pivots only when referring to base breakouts, but the neckline of a head and shoulders formation is also a pivot line.
A pivot for swing traders or trend followers has nothing to do with the definition found on Investopedia.com and cannot be calculated. In reality, the pivot price level is not an exact level either, but rather a small range, so don't be too strict. Intraday action around a pivot level is oftentimes meaningless and you should wait for the close and evaluate the situation on an end-of-day basis once the (intraday) dust has settled.
Unless specified otherwise, a pivot usually refers to a base breakout line. (See example #1).
Here are a few examples:
Example #1: Classical pivot in the form of a horizontal (or slightly sloped) base breakout line.
Example #2: Pivot as a neckline in a broader head and shoulders topping formation
Example #3: Pivot as a negative clothesline.
It's not rocket science.