There is good support that it probably means "shield" or "barrier" or "gate" or the like
I agree with Miles Bedinger's answer noting that dwarven words relating to "shield" start with "bar", and that this may be a clue to the semantics. To wit:
- barak: "backbone, strength, shield"
- barakor: "those who shield"
There are further considerations that support this conclusion. Based on various sources from earlier versions of D&D materials, these places were all originally established for the sake of their being defensible positions that controlled folks passing through to somewhere:
- Sundabar (originally called Citadel of Sundabarr) is on the Silverymoon Pass, a narrow pass through the Nether Mountains. Sundabarr was thus deemed "the rampart of the north, keeping the realm's dangers beyond civilized land."1
- Mirabar was positioned to block hordes of orcs from following the road that would reach the gem-rich Spine of the World mountain range.
- There are miles and miles of corridors under the Ice Mountains, and the only direct way to get in is through Adbar (unless you want to come through the Underdark). It was originally called the Citadel of Adbar.
- The key structural focal point of Felbar (originally called the Citadel of Felbarr) was a gate entering the Rauvin mountains called "The Runegate".
Incidentally, the surname "Barr" in English etymologically is related to "gate", and its meaning goes back to the Middle Ages when, like many old surnames, it represented one's profession; it was short for "Barrier" who was a "maker of bars," i.e., city gates. This may or may not be relevant to how the designers fashioned the dwarven language, but it's an interesting coincidence to say the least.
- Ed Greenwood and Jason Carl (July 2002). Silver Marches. (Wizards of the Coast), p. 65. ISBN 0-7869-2835-2.