That's an estimate given by W.W. Phelps for the age of the universe ("eternity"). Incidentally, "Gy" is the usual scientific shorthand for 1,000,000,000 years, because there is both a Short Scale and a Long Scale version of what a "billion" is. They differ, depending on the country you live in, by 1,000.
In The Times & Seasons, 1835, Phelps wrote "...that eternity, agreeably to the records found in the catacombs of Egypt, has been going on in this system, (not this world) almost two thousand five hundred and fifty five millions of years..."
A deeper probe suggests that Phelps came up with this number by multiplying
7,000 x 365 x 1,000 = 2,555,000,000.
In The Times and Seasons, he specifically said this was the age of the universe ("not this world"). This number also includes Phelps' assumptions that we are nearly at the end of eternity, that a day for the Lord was a 1,000 years to man, and that Genesis supported a 7,000 year span of creation. The current best estimate for the age of the universe - the time since the Big Bang - is about 13.4 Gy. You can tie yourself up in knots over this half-order-of-magnitude difference, but on the scale of important things, this ranks well below the noise threshold.
This 2.555 Gy number is nevertheless interesting. In a remarkable coincidence, the Great Oxygenation Event of the Earth closely brackets this age. Depending on who writes about this, the GOE started at 2.7 Gy or 2.5 Gy, or 2.4 Gy. Before that time, the Earth's atmosphere was largely methane, SO2, CO2, and ammonia. The sky was not blue, and the Earth would have been unrecognizable to us as such. There are deposits of alluvial pyrite (FeS) sand found in Archean rocks in South Africa that predate the GOE; the grains are rounded, something that could never happen in the presence of oxygen (they would turn rapidly to iron oxides, including rust, in the rough-and-tumble erosion and deposition process).
A talk given at one of the Union sessions at American Geophysical Union on December on 5 December 2011 fleshed out a lot of the chemistry necessary for oxygen to appear in the primordial Earth's atmosphere. First, a lot of hydrogen had to escape the atmosphere. This can happen when hydrogen-based molecules in the atmosphere decompose in the presence of U/V light - and in the absence of a protective ozone (O3) layer. Then, a lot of the freed-up oxygen would be needed to break down the remaining methane in the atmosphere. There is another big oxygen sink, however: the rocks of the Earth's crust themselves had to be oxygenized. Only then (after the oxygen sinks were filled) would significant amounts of O2 get into the atmosphere, and a significant amount reach the upper Troposphere and form a protective shell of ozone.
Somewhere in this evolving planetary atmosphere photosynthesis also began producing O2, but the atmospheric scientist at AGU discounted this as being a significant producer until after the Huronian Snowball Earth event.
Today, modern photosynthesis in plants could produce the 21% oxygen in the modern atmosphere in just 2,000 years. During the Cretaceous, the ultimate dinosaur wonderland (or nightmare alley, depending on your point of view), the atmospheric oxygen ranged up to 35% - which would go a long way towards explaining 22-meter-long dinosaurs and meter-long insects in the fossil record from this time.
The Earth's age may be around 4.5 Gy, but as we presently understand it, it is closer to 2.555 Gy.