The large number of Austrian archdukes comes from two potential sources. The first is the various divisions of Austria between brothers and other relatives of the Habsburg family, and the second is the use of the title "Archduke" as an honorary title for any in the immediate line of succession. For the former the first notable division was between the Albertinian and Leopoldian lines, following the death of Duke Rudolf IV in 1365, his two sons (as you might have guessed, named Albert and Leopold), divided up his lands between themselves. Before we get to far in, it's important to make a note on geography. While now we think of a unified Habsburg Archduchy of Austria, that territory was--itself--a composite realm. It included the Duchy of Austria itself, primarily centered around the Danube River valley, the Duchy of Styria to the immediate south of Austria, along with the Duchy of Carniola, the Duchy of Carinthia, and the County of Tyrol. While this map of Austro-Hungarian political borders does not map perfectly onto the older medieval borders, it does help to give you an idea of where the territories are located. Referring back to the Albertinians and the Leopoldian lines, after the death of their father, Duke Albert and Duke Leopold co-ruled for a few years, but ultimately decided to divide their territories amongst themselves, with Albert receiving Austria Proper, and Leopold receiving Styria, Carniola, Carinthia (usually lumped together as 'Inner Austria') and Tyrol, along with the old Habsburg lands further west (usually termed Anterior or Outer Austria). While the lands of "Austria" were all under Habsburg rule, they remained divided between the two lines until 1490, where the territories were reunited under Emperor Frederick III, who was of the Leopoldian line. However, this would not be the last time "Austria" was sub-divided among Habsburgs.

Charles V, the famous ruler of the whole Habsburg Empire effectively entrusted his younger brother Ferdinand I with rule of the Austrian lands and dvided the realm on his death. Charles's son Phillip received Spain and its colonies, as well as Habsburg holdings in the Low Countries and Italy. Ferdinand I, in turn, succeeded to the Austrian lands and was elected Holy Roman Emperor. On his own deathbed in 1564, Ferdinand I divided his realm amongst his sons. The eldest, Maximilian would take Austria Proper, as well as the Kingdom of Bohemia and the rump Kingdom of Hungary and was elected Holy Roman Emperor following his father's death. The middle son, Ferdinand would inherit Tyrol and Anterior Austria, and the youngest song--Charles would rule Inner Austria. Maximilian's line would remain the dominant line of the Austrian Habsburgs for most of the remaining 16th and early 17th centuries, with his sons Rudolf and Matthias also being elected Holy Roman Emperor. This division of Austria would lead to the so-called "Brother's Quarrel" between Rudolf and Matthias, which also drew in members of various other Austrian Habsburg lines. Charles's son, Ferdinand (the future Holy Roman Emperor Ferdinand II) would unite Austria under his rule in 1619, but he would later divide his realm again. The Austrian Habsburg lands would generally remain divided between two brothers or other branches of the family until they were firmly reunited under Holy Roman Emperor Leopold I in 1665.

Thus, the answer to your question of why there were so many Habsburg Archdukes throughout this period is that all of these divisions held the title "Archduke", and their lines continued with that claim. Thus, say--following Ferdinand I's division--you would have at least 3 members of the family fully entitled to the title "Archduke". These were all Austrian Archdukes, but not all Archdukes of Austria. Rather they were rulers of various pieces of Austria. Holy Roman Emperor Ferdinand II, for example, began ruled as Archduke of Styria, while his relative Holy Roman Emperor Rudolf II ruled as Archduke of Austria and Holy Roman Emperor. Later on--when I can't precisely say, but by the time of Austria-Hungary for sure--the title "Archduke" was generally used for everyone who was in the Imperial line of succession, thus creating a true plethora of Austrian Archdukes.

As for where the title "Archduke" came from in the first place, quite literally, the Habsburgs made it up for themselves to make themselves look more important. Rolling back to the 14th century, in 1356, the Imperial Diet under Holy Roman Emperor Charles IV promulgated the Golden Bull, which set up the constitutional structure of the Holy Roman Empire practically through to its dissolution. The Golden Bull recognised the seven Prince-Electors as the only ones who were entitled to cast a vote for Imperial succession, and granted the Prince-Electors, (the King of Bohemia, the Count Palatine on the Rhine, the Duke of Saxony, the Margrave of Brandenburg, and the Archbishops of Mainz, Cologne, and Trier) additional privileges which sat them above the other Imperial princes. In response to this, Duke Rudolf IV "found" (read, forged) the Privilegium Maius, which purported to grant the then Duchy of Austria with a number of privileges that made it equal to the other Princely electors. One of these was the title "Archduke Palatine", which would later be adopted by nearly all Austrian princes, as discussed above. The Privilegium Maius was recognised as a forgery at the time, but that didn't stop later Habsburg princes from insisting on the title and additional privileges. When a Habsburg again regained the Imperial seat, Holy Roman Emperor Frederick III in turn recognised the Privilegium Maius on his election in 1452.

I hope this has helped answer your question, and please feel free to ask any follow ups.