A magical staff is an object which some sorcerers use to perform magic, enhance their magical abilities and it's used as a weapon. Like general spells, these sorts of magical instruments are used to channel one's magic, focusing it on the object of the enchantment. They are usually sources of magical strength, too.
All the Sidhe possess Sidhe staffs that they use to cast bolts of magical energy or perform the different spells of Sidhe magic. Even when a Sidhe is banished from Avalon, he cast still keep his staff, along with his magical powers. Gifted human sorcerers can harness these staffs' powers to their own.
Morgana used the Rowan Staff which was carved from the Rowan Tree that grows on the Isle of the Blessed so that she would raise an army of skeletons. The staff's power was powerful enough to guide its user so that they would not have to chant a spell and only the High Priestesses and their Blood Guard had set eyes on it (The Tears of Uther Pendragon: Part Two).
The Cailleach owned a magical staff, too. She may have used it to control the Veil between the Spirit world and this world, closing or opening it at her command. However, she was only seen using it against Gwaine, casting a stunning spell with it. And in Morgana's vision, Emrys was seen walking with a long, white staff, that could have been magical (The Darkest Hour).
Alator of the Catha also possessed a magical staff. Being him a warrior and a priest, his staff could also be some kind of weapon. He used it a source of magical power to blast Morgana against a wall, defending Merlin (The Secret Sharer).
When Gaius and Merlin went to visit the druid shrine in the woods, the old physician took a white staff with him. It's unknown whether this staff was an instrument of magic from the days when Gaius practiced magic, or just a normal walking staff. However, it is likely that it was a walking staff; he could either have been using it because he was recovering from the events of Alator of the Catha's torture, or because he was simply aging (A Herald of the New Age). Gaius used another staff while searching with Merlin in the woods outside Camelot for evidence that would lead to the identification of the new traitor in the castle (A Lesson in Vengeance). He was also seen using a walking stick in "The Diamond of the Day: Part Two".
The three soothsayers that formed the sacred court of the Disir carried one magical staff each, which, according to Gaius, had been forged using powerful sorcery. The priestesses created the runemark Osgar gave Arthur by dipping their staffs into a dark pool while chanting a spell.
When the knights of Camelot threatened them, two of the seers threw their staffs; while the first one hit and inflicted Sir Mordred a terribly serious wound, the second one was put off course by Merlin's magic. Mordred was taken back to Camelot, but when Gaius saw the boy's condition, he told Merlin that only his powers could have saved him. Since the young warlock refused to save the life of the person destined to kill Arthur, the old physician made the King believe that only the Disir could undo their own magic (The Disir).
When Emrys used magic to free himself from the magical trap Morgana had conjured to imprison him in the Crystal Cave for eternity, he was in his aged form, wearing red robes and with a white staff, the same Morgana had seen in her vision, in his hand. From a cliff overlooking the Plane of Camlann, he used his staff to cast deadly lightning spells which destroyed the High Priestess' army (The Diamond of the Day).