The Spartans are known for different things to different peoples in time. Some of these things are good, and others bad.
Today, if you ask a typical 20-something man who has a keen interest in history, watches historical movies and plays historical video games, he will say that the Spartans are best remembered for their Military prowess. It is this quality that will stand out most to him.
If you ask a modern day politician, he may say that the Spartans are best remembered for their ideals of Liberty and their persistence to remain an independent free people. Liberty from the Persians, Athenians, Thebans, Macedonians and Romans.
If you ask an 19th century British scholar, he may say the Spartans are best known for their ideas of beauty, heroism, physical athleticism, reverence of the Gods (eg not fighting on holy days etc) and other romantic ideals.
If you ask a sociologist, he may point out that Sparta's treatment of women was better than in most other places in the Greek world. They may point out that Women could become quite successful and famous in Sparta (eg Cyniska, Gorgo etc).
If you ask a Greek today, he may tell you that the Spartans form part of their cultural heritage and are an important part of Greek history. Spartan symbolism such as lambda shields and Corinthian plumed helmets are a common feature of Greek art and media.
If you ask an ancient Persian, he may say that the Spartans are remembered for their insolence, persistence and rudeness. They may also be remembered as gold-hungry traitors who would betray their fellow Greeks for a few coins.
If you ask an ancient Macedonian, he may call them insignificant mice (As did Alexander the Great) who care only about themselves.
Ancient Athenians would have called them uncultured barbarians. The bullies of the Greek world.
If you asked the Romans, they would have called them inspiring and worthy. They would have called them people to look up to.
The history of the Spartans is long, complicated and contradictory. The imprint they have left in western civilisation however is significant and in my opinion, ever lasting. In my opinion, you should tell your daughter that they where a tough society that did not mess around and got things done no matter the cost.
For more on Sparta, I would recommend starting with this book by Paul Cartledge