A way to drill down and see how much time has expired between two timestamps (integer).

time_parser

module Duration

  def self.calculate(duration)
    times = {years: 31536000, months: 2678400, days: 86400, hours: 3600, minutes: 60, seconds: 1}
    response = ''
    duration = duration
    times.each do |time, value|
      numerator = duration / value if duration >= value
      duration = duration % value if numerator
      response << "#{numerator} #{time} " if numerator
    end
    puts response
  end

end

Duration.calculate(99720045)

Great start.

Suggestions:

Your hash syntax is not supported by ruby versions < 1.9. (This matters if you're going to make a gem.)

In math the word numerator has a specific meaning (e.g. the top portion of a fraction) and in this example the word quotient would be better.

What happens in these cases:
calculate(99720045.0)
calculate(nil)
calculate(-1300) # this is a possibility if you subtract the times in the wrong order

When I Google "days in a year" it says 365.242 but you're assuming 365.

I'd change "times.each do |time, value|" to:
time_buckets.each do |time_description, time_in_seconds|

I'd also change the time integers to have an underscore at every 3 numbers e.g. 31536000 => 31_536_000

Correctly pluralizing the words would be good too, like you said.