An ageing spell allows the caster to age himself so that he appears physically older. Ageing spells can be considered advanced forms of another kind of spell, the glamour, and are notoriously difficult and unpredictable.
It's not clear if the warlock or witch can control the spell and decide how much to get older. When Merlin used this spell, he turned into an 80-year-old man, declaring before that it was his intention to get this old.
Use by Merlin
Dragoon the Great
In his chambers, Merlin prepared an unknown powder that he threw in a cauldron while he chanted: "Miht dagan, beþecce me. Adeadaþ þisne gast min freondum ond min feondum". The powder exploded and as white smoke rose to his face, Merlin transformed into an old man.
He was purposely caught by Arthur Pendragon planting a poultice but he was unable to then escape, as was his intention. Merlin tried to break the spell (with the incantation "Edniwe min geoguð"), but it was too strong for him.
Merlin was moments from being burned at the stake when Gaius finished working on an antidote which the young warlock was able to seize in the commotion caused by a fire spell and then consume as he fled the scene, changing him back to his former self (Queen of Hearts).
Merlin used this spell again to transform himself into "Dragoon the Great" when Arthur was willing to use magic to save his father's life. This time Merlin had Gaius prepare the potion that could reverse the effects of his spell so that he would not be trapped in this form. Merlin also cast the spell in a different way, only chanted the words of power of the Old Religion, without any magical potion (The Wicked Day).
The third time Merlin used this spell was when he sneaked into Morgana's Hovel to steal and then kill the Fomorroh that was controlling him. This time his old age caused him to be rather slow when he tried to run away from her and suffered greatly because of the stunning spells Morgana put on him. His magic (a whirlwind spell, in particular) was still too powerful for Morgana to beat (A Servant of Two Masters).
Merlin used again this spell when he entered the castle of Camelot, after it had been conquered by Helios and Morgana, to put an enchanted poppet under the High Priestess's bed. It seems that this time Emrys didn't need Gaius'; potion to turn back into himself (The Sword in the Stone: Part Two).
The young warlock turned to his "Dragoon" persona again after he was framed of having poisoned the King by Guinevere, who had been brainwashed by Morgana and become her ally. Gaius lowered the potion used for breaking ageing spells into the cell Merlin was kept in, and the sorcerer escaped in his aged form. After a couple of quarrels with two guards and the cook Audrey, Merlin broke the enchantment and turned back into himself, just in time to save Arthur's life (A Lesson in Vengeance).
When he went to the Dochraid's lair in search of information regarding the way of freeing Queen Guinevere from Morgana's control, Merlin disguised himself as Old Emrys again, to make sure the old hag could not recognize him. However, when the blind Dochraid asked the sorcerer to give her his hand, she smelled the stench of enmity and realised who he was, the warlock Emrys who was no friend of Morgana Pendragon nor of the Old Ways (With All My Heart).
In the Crystal Cave, before parting again, Balinor's spirit told Merlin that he was yet to discover his true power, which could only be revealed in the heart of the Cave. He told him to step into the light and trust in what he was and would always be, for Merlin's end would never come. When he magically broke through Morgana's prison, Merlin was revealed to have turned into his older self, with renewed strength and eternal life. In this shape, the everlasting sorcerer went to the battlefield of Camlann and destroyed the High Priestess' army with his tremendous magical powers (The Diamond of the Day).
To save Queen Guinevere from the Teine Diaga, the "sacred fire", a ritual of the Old Religion which used the mandrake root to bring unimaginable terror to its victims, destroying their will and making them slaves of the High Priestesses for eternity, Gaius convinced King Arthur to fight sorcery with sorcery and to go to the ancient sorceress of the Cauldron of Arianrhod, whose waters could heal Gwen's spirit and free her from Morgana's control.
The old sorceress was, in reality, Merlin himself, who was using a very particular type of ageing spell, which allowed him not only to age his body but also to turn into a woman. Although the warlock did manage to rid the Queen's soul of Morgana's dark magic, at first he was very worried because he feared he could not have both held the exhausting ageing spell and summoned the White Goddess herself (With All My Heart).
Use by Morgana
After conquering the kingdom of Nemeth, Morgana came up with a plan to infiltrate Camelot and lead Arthur into a trap. She cast an an ageing spell on herself and disguised as "Hilde", pretending to be Princess Mithian's maid. However, Mithian was under the Priestess's control, who kept her locked in her room, threatening her, even by using magic to torture her, that if she hadn't cooperated and kept lying to Arthur, she would have killed her father, King Rodor.
Morgana's ageing spell was very powerful, and the witch demonstrated how strong her magic was by being able to hold such an enchantment for a very long time. However, this form of magic took its toll and Morgana suffered from sudden spasms of pain, which exhausted her. Even when she broke the spell and turned back into herself, she was overcome by attacks of pain. Another minor flaw in this spell was that it didn't alter Morgana's body entirely: as Gaius realized when he tried to cure Hilda from one of her attacks of pain, her blood flowed in her veins with the strength and vigour of a young woman.
Another difference between Morgana's enchantment and Merlin's was that the High Priestess didn't need to drink or use any sort of potion to transform into an old woman or to change back into herself. Each night, while Mithian and her were still in Camelot, she broke the spell and assumed her usual aspect, probably because it was too painful to always be under the ageing spell's effects (Another's Sorrow).
In the episode "A Lesson in Vengeance", Morgana used this enchantment again so that she could have met Guinevere, who had become her ally after having been brainwashed by the sorceress' dark magic, in the market outside the castle. The disguised witch gave the Queen a vial of valerian, two drops of which could render the victim unconscious and another of henbane, which, if a single drop would be administered through the ear, could give a prolonged and unpleasant death. Gwen used these potions to poison the King.
It is possible that Morgause used an ageing spell as well to take on the form of a poor old beggar woman so that she could have met with Morgana in the city market. Her spell wasn't as powerful as Merlin's, for her true form could be revealed in a mirror. This may indicate that this enchantment wasn't a real ageing spell, but just a glamour (The Eye of the Phoenix).