We know how fast light travels and how distance is measured in astronomy. They often use light years, because kilometers sound absurd. For perspective, one light year is equal to 9.461 trillion kilometers. For astronomy to claim that the distance to the nearest star system from the Sun, Alpha Centauri is 4.37 light-years is equally incomprehensible to any mind as the claim of billions of years. When one says that the Big Bang happened over 13.7 billion years ago and the current radius of the universe is placed at 46.6 light years (over 441 trillion kilometers), those numbers do sound abso-freaking-lutely unbelievable! Why do they use such numbers?
Science needs measurements. Why do we believe and agree that there are over 7 billion people on Earth? Can you comprehend a mass of people that large? Say you have a billion dollars cash in denominations of one dollar notes, can you comprehend that amount of cash? Mathematics is a language that affords us the scales of numbers even when such numbers are incomprehensible. For example, using scientific measurements, it has been estimated that the age of our planet Earth is at around 4.54 billion years. Radiometric dating techniques are used to get those numbers to an agreeable degree of accuracy. It is the same such techniques used to estimate the age of fossils. Currently, it is the most accurate method available for such long periods of time. It allows us to put things in perspective.
So what is a billion years? I do agree that a billion years can not be observable, with the angle that our grasp of observable time is so small to put a billion years in perspective. However, as I said earlier, time can in fact be measured and therefore even if the numbers sound absurd, it is what gives us perspective of the vast amount of time that has passed since certain events occurred throughout our history. A billion years have 31,536,000,000,000,000 seconds! That's only 3.1536 x 10^16 seconds! In mathematical language, I can very much comprehend that.