The Malcolm in question is Malcolm III (1031-1093), later nicknamed Malcolm Canmore, who ruled Scotland from 1058-1093.
Malcolm’s father, Duncan was king of Scotland until 1040, when he was killed in battle fighting against Macbeth. Macbeth became king. At the time Malcom was only nine so he was sent away from Scotland for his own safety. There were then a series of attempts by the family to overthrow Macbeth, who was finally killed in 1057. His stepson succeeded him, briefly, but after six months was also killed. After that Malcolm was crowned king of Scotland, in 1058.
Malcolm did not rule over the whole of modern Scotland: the North-West was under Scandinavian rule. To the south he initially tried to take advantage when Northern England rebelled against William the Conqueror, but eventually he and William negotiated a peace. After William the Conqueror died and William Rufus was crowned Malcolm visited England to renegotiate the peace. However, the talks broke down, Malcolm returned to Scotland, gathered an army, and began to harrow Northumberland.
On the second invasion in November 1093, his army was besieging Alnwick Castle when they were surprised by the army of Robert de Mowbray, Earl of Northumberland. In the subsequent battle Malcolm and his son and heir, Edward, were both killed.
A cross was erected to mark the site of the battle, and some broken remains of that early cross can still be seen. The cross in the picture was erected later, in 1774, by Elizabeth, Duchess of Northumberland, the wife of the First Duke.