2^79 is the number 2 multiplied by itself 79 times. This is a very large number, which would be expressed in scientific notation as 6.0446291 × 10^23, or 6,044,929,100,000,000,000,000,000. Or, around 6 septillion.
There are many big numbers out there, many bigger than 2^79. So what is so important about this number? This number is the first power of two over Avogadro's Number, and is actually quite close to it, only being about 3% more. Avogadro's number is the number of atoms in a mole of some substance. So 2^79 is the power of two that is closest to Avogadro's number.
The relevancy of this comes up in a discussion of radioactivity and the half-life of various isotopes. A half-life is the amount of time that half of an isotope will decay in, and since 2^79 is equal to Avogadro's number, it therefore takes 79 half-lives for a mole of a radioactive isotope to totally decay. Thus, to find out how long before a mole is totally, completely gone (statistically speaking), just multiply the half-life by 79.
For example, Flourine-18, used as a radioactive tracer in medicine, has a half-life of 110 minutes, and therefore a mole of the material would be gone in 8,690 minutes, or about 6 days. Iodine-131, which can be released during malfunctions at nuclear power plants, has a half life of 8 days, and thus would be totally gone in 632 days, or a little less than two years. On a longer time scale, an isotope such as Potassium-40, with a half life of 1.25 billion years, would take over 100 billion years to totally disappear. Further examples are easy enough to find, since they just involve finding a half-life and multiplying it by 79.
There are a few things to be mentioned about this. One is that the amount of atoms in a mole is rather arbitrary, and therefore there is nothing magic about the 79 half-lives. It is just a good yardstick to begin with. For example, in the example of Fluorine-18, there is hopefully much, much less than one mole being used to test. And in the example of Potassium-40, there are many trillions of moles present in the earth, so it will take longer than 100 billion years before the last atom has disappeared. However, the half-lives per mole is a good yardstick to begin with.
The other thing to remember is that the time before the isotope is totally gone is much greater than the time before its effects are minimal or undetectable. Atoms are very small, so even sophisticated equipment would be unable to detect traces of a radioactive isotope long before it had gotten through its 79 half-lives. For example, Plutonium-244 has a half-life of 82 million years, and so therefore some Plutonium-244 from the creation of the earth is still present, although for all practical purposes, it is no longer present.