Final answer:
The galaxy's emitted light being measured at a longer wavelength on Earth than its original wavelength indicates that it is receding, demonstrating a redshift due to the Doppler effect.
Step-by-step explanation:
The observation that the wavelength of light from a distant galaxy has increased from the originally emitted 586.9 nm to 588.6 nm when measured on Earth indicates that the galaxy is receding from the Earth. This phenomenon is known as redshift, which occurs due to the Doppler effect as the galaxy moves away, causing the light's wavelength to stretch and shift towards the red end of the spectrum. The greater the redshift, the faster the galaxy is moving away from us, contributing to our understanding of the expansion of the universe.