Shigesato Adachi was a member of Clan Adachi of Tsushima and son of Lord Harunobu Adachi and Lady Masako Adachi. He and his brother Yasunari were hanged by Mongols following the Battle of Komoda Beach, where their father was also killed.
In traditional Mongolian culture, killing a noble by shedding blood is insulting and thus forbidden, hence their execution by hanging. In traditional Japanese culture, this is insulting however, as the two samurai brothers are denied the dignity to commit seppuku, hanging them implies they are mere criminals.
Their mother Masako was understandably devastated and lamented how they were "strung like animals".
Back when the Adachi brothers were alive, they wished to be buried in Adachi Estate, but Jin warns Masako that the journey would be far too dangerous. Masako then suggests burying them at the nearby Komoda Lighthouse, as her sons loved to play there when they were younger.
Some time after the battle and the concurrent Adachi massacre, Masako has a set of armor that belonged to Shigesato repaired, and gives it to Jin Sakai.