The 125 mOhm ESR is the key number for the BOM: it limits the ripple current the cap can handle before self-heating becomes a derating issue. For a 100 kHz buck output, the ripple current squared times ESR must stay below the thermal budget of the D-case 2917 package — a 500 mA ripple produces about 31 mW of internal heat, well within the molded case's dissipation capability.
This cap can sit on a satellite PSU board that cycles from cold-soak to component self-heating, or on an outdoor telecom rectifier exposed to desert sun. The molded case and the 35 V rating give it margin against the 28 V bus in avionics.
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The TPS series is a standard molded tantalum line, widely second-sourced by Kemet and Vishay, but this exact order code is KYOCERA AVX's own.