It would be incorrect to assume that
every change has a significance
from an evolutionary point of view. In many cases, the changes could be happening at an age where it does not affect it's selection, since it's past the reproductive age. This could certainly be true for greying of hair.
If you want to understand from the point of view of an evolutionary theory, there are at least two possible explanations. One is the Mutation Accumulation (MA) theory. It says that mutations causing late life deleterious effects can build up in the genome more than diseases that cause early life deleterious effects. This is for the simple reason that cases of the latter would be eliminated as they will usually affect in the reproductive period, but chances of a 60 year old grey-haired man to have offsprings is low. In essence, if a trait reduces survival in the post-reproduction period (which is the case here), then the effect of selection is weak for it. So, since grey hair arrive so late, they might not really be selected out.
Another is the Antagonistic Pleiotropy theory. Pleiotropy means a single gene having more than effect. So it says that if a gene improves fitness early on, but causes an undesired effect later in life, it will be selected for in the population. This is simply because the later deleterious effect does not affect the advantage the gene provides at the stage were reproduction happens. So, it is possible that the gene responsible for grey hair may also be making you more fit.
So, in summary, there seems to be no direct advantage of having grey hair. It could be the result of Mutation Accumulation, or the antagonistic pleitropy effects of the responsible gene.
You can read more about it in this and this answer.