The monetary unit assumption is that in the long run, the dollar is stable—it does not lose its purchasing power. This assumption allows the accountant to add the cost of a parcel of land purchased in 2013 to the cost of land purchased in 1956. For example, if a two-acre parcel cost the company $20,000 in 1956 and in 2013 a two-acre parcel adjacent to the original parcel is purchased for a cost of $800,000, the accountant will add the $800,000 to the land account and will report the land account's balance of $820,000 on the company's balance sheet.
To say that the purchasing power of the dollar has not changed significantly from 1956 to 2013 is quite a stretch. However, the assumption is that the purchasing power of the dollar has not changed.
Part of the monetary unit assumption is that accountants report assets as dollar amounts, rather than reporting in detail all of the specific assets. If an asset cannot be expressed as a dollar amount, it cannot be entered in the general ledger. For example, the management team of a very successful corporation is by far its most valuable asset. However, the accountant is not able to objectively convert those talented people into a dollar or monetary amount. Hence, the team will not be included in the amounts reported on the balance sheet.