Sparta was one of several Greek city states in the 1st millennium BC and among the most powerful in that region. It was notable for stratification (With Spartiate upper class, Perioeci artisans and merchants and Helots, agricultural slaves) and of the extreme level of militarization it had among its ruling class. With the exception of the heir apparent, the entire male Spartiate class was subjected to a brutal training regimen from childhood called the Agoge and then required to serve as kill squads against their Helot Farmers and then soldiers in the spartan army before being able to marry and after that would drill constantly. This contrasted with the armies of the other greek city states. These were composed of informal forces civilian militia drawn from the general population who were expected to train and equip themselves.
This system did produce the best Hoplites in Greece (for a time at the least) as they held formation for longer and breaking formation in Hoplite warfare was just another way of saying "lost" as well as being effective against the armies of the Achaemenid Empire, which was to be expected given that civilian hoplite militia did well against Achaemenid armies. That said would ultimately prove to be their downfall. Since they were constantly killing their kids there was never more than about 8,000 of them at one time and the only way to get new ones was by reproduction. The Helots, which outnumbered the Spartiates considerably and did not like being constantly under their heel or having to put up with armed teenage wankers trying to kill them and other such bullshit were constantly rebelling and needed constant attention to be kept in line. They soon pushed themselves to their limit and afterwards their numbers dwindled away and were eventually defeated. The end of their prominence happened famously by Theban general Epaminondas at Battle of Leuctra and finally by the Macedonians and Romans, which could mobilize their various conquered peoples to provide vast numbers of soldiers.
To add insult to injury the Theban army that broke the Spartiates were using a similar training only not as brutal, named the Sacred Band which was 150 gay couples hand pick based solely on skill form their normal hoplite militia.
Legacy in Fiction
The Spartan trope in fiction refers to any army or military force that relies heavily (or completely) on brutally trained soldiers to do their work, rather than having a balance of rank-and-file troops and special forces. So they have a small band of elite soldiers that're more than a match for any soldier, but have very limited numbers, in comparison to other armies in the setting.
It should be noted, however, that most fictional examples are of an elite force supplementing a greater army of mooks, rather than composing one's entire military force of a small number of elite soldiers that take a long time to train. Which is exactly what Sparta did.
Examples of such training programs include...
- Sardaukar from Dune
- Spess Merhens in Warhammer 40,000
- The Clans from Battletech
- The child soldier program in Metal Gear universe. Raiden is one of the notable example. Grey Fox is from a different but similar program than Raiden.
- There are other variations created by the patriots, like the Genome Soldiers. It is a lot similar to the star wars stormtroopers down below (only Boba Fett is replaced by Big Boss for gene cloning). The well known Les Enfants Terribles project utilizing the super baby method. Using both Eva's womb and big boss's gene that gave birth to badasses like Solid snake and Liquid snake.
- Later on they just said fuck it and started using VR training and nanomachines to program soldiers. Later on in Metal Gear Rising, children of other poor third war country were kidnapped and their brain were put into some sort of simulator where they play Warhammer 40,000 Space Marine in actual experience(with pain and all that). The children's brain were then put into a cyborg body as a "graduation present."
- Spartans (not even trying to be subtle) from Halo.
Though it should be noted that the program was impracticalthe Spartan II program was effective it just took eight years and as much money as an entire unsc fleet. The later Spartan IV program did away with the Spartan way and is much more cost effective (yah spartan IIs and IIIs rip through IVs). (why dose no one remember the IIIs they actually outperformed the IIs and IVs while costing a lot less) (I'd question that, the IIIs were meant to be disposable ones & most don't even have energy shielded armor. Their advantages are numbers, ease of production & generally a "More but weaker" mentality. Of course, they're also the least publicized IRL as IIs have virtually all of Halo & the IVs have Halo 4 onward. What do IIIs have in comparison, Reach? Even that was a highly exceptional team with equipment equaling the IIs including one II in the team. The average Noble Team member is leaps beyond the average III.)
- Star Wars Stormtroopers, really. Only the cloned ones, though. The academies that produce officers for the Imperial Army and Imperial Navy also produce Stormtrooper Corps privates (and some, such as Carida, specialize in that).
This does not mean that you won't end up with several hundred extremely capable, elite warriors. You'll get your fighters, most certainly, but you'll also have the corpses of many more who have taken up valuable resources that could have been more normal warriors. Additionally, a force this small will be highly vulnerable to an enemy that relies on attrition tactics (I.E: Wearing down the enemy with prolonged warfare), as the spartan-type army simply will not be able to keep up the fight against an enemy who can easily replace their losses in quick succession.
Overall; Having elites in any army is good strategy, basing your entire army on elites alone isn't.