*ambhi-

This core idea of this root was:

around, from both sides

It’s probably based on the root *ant, which was about the side, the end.

The original idea is still quite visible in offspring like ambiance, amphitheater or ambiguous.
But there’s way more. There are plenty of words in English where the original idea is more or less obscured, like ambitious or embassy.

And the two syllables of ambhi actually also went their own separate ways. The first one is the origin of German um, which focused on the sense of around.
And the second part is the origin of by, bei and the German and English prefix be- which in a VERY abstract way is about direct impact (from all sides).

Here’s an incomplete list of English family members with a little idea how it could tie in with the origin:

• ambiance (“all around around us”)
• ambiguous (“two meanings”)
• ambition, ambitious (“ambi” + “ire”, originally “going around”. Think of being busy.)
• embassy, ambassador (“send out and around”)
• but (“by+out”, originally introducing an exception)
• about (“overview from the outside”)
• by (“near, close to” from originally “around”)