Year is what we define it to be. For us as humans it was easy to set a year relatively to the cycle of seasons. Only later that we found out that a year is how long it takes for the earth to go around the sun.

So you see, every planet has its own year, its own orbital period. Venus year is 255 earth days, what with it being closer to the sun.

Neptune being so far, it's year is as long as 165 earth years.

The reason we look at the age of the universe in time relative to us – to the earth year, is because it's much easier to conceptualize it, instead of spending time inventing a new unit of time.

Even speed on a galactic level we measure in the distance light travels in an earth year.

So, was a year different in different times?

actually... yeah, though not how you might think. Different calendars had slightly different day counts for years. For instance, old persian calendars had 360 days in a year. The old roman calendar – before the introduction of the Julian calendar was 304 days long. When transitioning to the Julian Calendar there was a transitional year with 445 days.

But when speaking of age of the universe, people refer to it as it is today – 365 days per year –> 24 hour per day –> 60 minute per hour –> 60 second per minute. a Second scientifically defined in relation to the frequency of a caesium 133 atom.

So the year one of the universe, is the same year you expirience today.