Q. What does "cut into thirds mean"? I don't know what a third is!
Again math rears its head in the cooking world! Is there no refuge? This and we're certain you're writing from a country where English is seldom spoken just means to cut something into three equal parts.
You may be making a large bread recipe, and need to shape the dough into three loaves. If you cut the dough into three essentially equal portions, they will all bake at the same rate, and your loaves will come out perfect. If you cut it into three unequal portions, the larger loaf will take longer to bake and you run the risk of overcooking the smaller loaf if you leave them in the oven for the same amount of time.
For the record, to halve something means to cut it into two equal parts. To quarter something means to cut it into four equal parts. Any fraction higher than that and you should think about finding a different recipe.