Although the observable universe is indeed finite, we are still able to observe distant galaxies due to the expansion of the universe and the finite speed of light. The light from distant galaxies takes time to reach us, and as the universe expands, the light waves are stretched, causing a phenomenon called redshift.
As a result of redshift, the light emitted by distant galaxies appears to be shifted towards longer wavelengths, shifting them towards the red end of the electromagnetic spectrum. This allows us to detect and study the light from these galaxies using telescopes and other observational instruments.
The observable universe represents the portion of the universe that we can currently observe given the age of the universe (approximately 13.8 billion years) and the speed of light. However, it's important to note that the actual size of the universe is believed to be much larger, and there may be regions beyond the observable universe that we cannot currently detect due to the limitations of our observational capabilities.