Samurai swords are those used by samurai in feudal Japan. Typically when someone says "Samurai Sword" what they are really referring to are katanas. Katanas are curved single-edged swords that were typically used by Japanese samurai. Other "Samurai Swords" would wakizashi, which are smaller than katanas, and tantos, which are mere knives.
Although they are not technically "Samurai Swords" we group ninja swords in this same category. Samurai were honorable warriors and ninjas were the oppsite, though they are from roughly the same time period. The ninja sword is straight, and not curved like a samurai sword.