Ooh, fun history of mathematics question.

First off, the word “percent” literally means “parts per hundred”. It’s a contraction of the Latin per centum, “by the hundred.” So, one hundred is the maximum percent because 100% is literally one hundred parts of one hundred. The term itself first shows up in the 16th century and quickly got abbreviated in English as per cent. (with a period, as it was an abbreviation). Later, we dropped the period and smushed the two words together.

You can also think of it as a fraction (because it is). 1% is 1/100. 25% is 25/100 (which reduces to ¼), 100% is 100/100 (which reduces to 1).

In mathematics, other “parts per X” do come up. Parts per thousand is “per mille” and the symbol is ‰. Parts per 10,000 is the concept of a “basis point”, abbreviated bp. It’s one hundredth of one percent. Parts per 100,000 is “per cent mille”, abbreviated pcm. Beyond that, the abbreviation is typically “pp_” meaning “parts per [bank]” (ppm, parts per million; ppb, parts per billion, etc.). Parts per million and per billion show up all over science all the time. Trace gasses in the atmosphere, disease rates, chemical concentrations, the list goes on and on.

Historically, before the mass popularization of decimal systems (an in particular, the Indo-Arabic system we use today), calculations were done very frequently as fractions. Halves, quarters, and, yes, parts per hundred. Using parts per hundred in calculations is ancient. Emperor Augustus levied a one part per hundred tax on auctions, for example. But, percent really started to get popular is the late 15th century and into the 16th with the proliferation of modern banking. Profits, losses, and interest rates started to be given in parts per 100. And thus, percent and percentages entered our daily lives.

u/Dashukta's answer describes percent and per mille well. All of these refer to how much something makes up of the whole, how large of a portion of the total we're looking at.

Since you asked about alternate maximums, I'd like to point out a few that are still in use today:

• Percent, as discussed, is x/100.
• Proof is x/200, meant for measuring the alcohol content of a drink. 100 proof whiskey is 50% alcohol. 200 proof is pure alcohol with nothing added, or 100% alcohol.
• Karat is x/24, meant for measuring the amount of gold in an alloy. 12 karat gold is half gold, half something else. 18 kt gold is 75% gold.
• Nines are 1-10^x, which probably doesn't help explain anything. One nine is 90%, two nines is 99%, three nines is 99.9%, and so on, reducing the remaining amount by 1/10 each time.

Because these other terms are limited to certain fields, you can't easily refer to say, Bacardi 151 as approximately 18 karat alcohol or 0.61 nines pure alcohol (as fun as that might be).