how did it get its name?
Lund named it Smilodon populator which the Ancient Greek meaning of "Smilodon" as ("smilē"), "scalpel" or "two-edged knife", and "οδόντος" ("odontús"), "tooth".
Smilodon
"Smilodon populator" in 1842. He explained the Ancient Greek meaning of "Smilodon" as ("smilē"), "scalpel" or "two-edged knife", and "οδόντος" ("odontús"), "tooth". This has also been translated as "tooth shaped like double-edged knife". 
when did the saber toothed cat become extinct It became extinct 10,000 years ago in the Quaternary extinction event. what is smilodon? is a genus of the extinct machairodont subfamily of the felids. how does it look like? It is well-developed forelimbs and exceptionally long upper canine teeth and its jaw has a bigger gape than that of modern cats.
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Smilodon [SEP] Taxonomy
Lund originally wanted to name the new genus "Hyaenodon", but realizing this had recently become preoccupied by another prehistoric predator, he instead named it "Smilodon populator" in 1842. He explained the Ancient Greek meaning of "Smilodon" as ("smilē"), "scalpel" or "two-edged knife", and "οδόντος" ("odontús"), "tooth". This has also been translated as "tooth shaped like double-edged knife". He explained the species name "populator" as "the destroyer", which has also been translated as "he who brings devastation". By 1846, Lund had acquired nearly every part of the skeleton (from different individuals), and more specimens were found in neighboring countries by other collectors in the following years.