Reference: Metheg-ammah
Easton
bridle of the mother, a figurative name for a chief city, as in 2Sa 8:1, "David took Metheg-ammah out of the hand of the Philistines" (R.V., "took the bridle of the mother-city"); i.e., subdued their capital or strongest city, viz., Gath (1Ch 18:1).
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Fausets
2Sa 8:1. Not in the parallel 1Ch 18:1. The name Metheg-Ammah must have fallen into disuse, originally designating the region wherein Gath was. Rather it is figurative: "David took the bridle of the mother (Gath the metropolis, i.e. wrested the supremacy) out of the hand of the Philistines." The Arabic idiom for submission is to give up one's bridle to another. The phrase "Gath and her daughter towns" (Hebrew, 1Ch 18:1) favors the rendering "mother." Gath became tributary to David.
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Hastings
David took Metheg-ammah out of the hand of the Philistines' (2Sa 8:1 AV and Revised Version margin). RV tr 'the bridle of the mother-city,' which has been interpreted to mean authority over the metropolis, or the suzerainty exercised by the Philistines,