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The original meaning of billion, established in the 15th century, was a million of a million (1,000,000 to the power of 2, hence the name billion), or 10 to the power of 12 = 1 000 000 000 000.
1 billion seconds is a significant birthday or anniversary, being about 4 months shy of 32 years. 1 billion seconds is 31 years, 251 days, 13 hours, 34 minutes, 54.7843 seconds. But note that these are 365-day years, so you have to adjust for leap years. Remember, a leap year adds 1 day at the end of February on years that are divisible by 4, unless they're also divisble by 100, except when it's also divisible by 400.