Reentry refers to a permit that visa holders other than tourists must buy. For example, if you are a work visa holder, you need to buy a 4000 yen single-use reentry permit or a 6000 yen multiple-use reentry permit in order to come back to Japan without voiding your visa.
As a tourist, unless you are from a country that actually requires a tourist visa (most don't because the passport serves well enough), you won't need to bother with a reentry permit.
Not sure what you discussed with the travel agent. People who come and go into Japan are sometimes considered suspicious types, depending on various circumstances. Come often enough, or soon enough after leaving, and immigration may wonder what you are up to. Trafficking? So, they may turn you down.