On macOS this arrow just appears, and overlays on top of any window.
How can I get rid of it?
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The floating arrow can appear whilst using the Help menu to point out menu items in Finder, and in other apps. The example below is from Finder, but I tried this in Pages and Keynote and the function/appearance is the same.
In this screenshot, the arrow is white, not blue. The arrow is animated and moves around a bit to give a visual hint it is active. Does the blue arrow move around a little when it is visible?
I searched for the single letter 'k' at random, and it found three menu items with 'k' in the title. I chose 'Sort By > Kind' and it opened the View menu and popped up the arrow to point at the Kind menu item.
Looking at Activity Monitor when the arrow appears shows that the WindowServer process CPU% increases, and decreases when the arrow disappears.
As to why this is happening to you, I have no idea, but at least this may be a clue to find out what is happening.
(My 2019 MBA is running Mojave 10.14.6)