275/60R15 is 0.94" taller than 255/60R15, a +3.49% change in diameter. That is more than the 3% many tire shops use as a limit, so plan on recalibrating the speedometer and checking ABS and stability control.
Ground clearance changes by 0.47" (half the diameter change), and the tire needs 0.47" more room above it.
275/60R15 is 0.79" wider. On the same wheel offset about half of that, 0.39", moves toward the suspension and half toward the fender.
Both fit a 15" wheel; the sidewall is 0.47" taller on 275/60R15.
Details: 255/60R15 in inches · 275/60R15 in inches · change sizes in the calculator