In The Lord of the Rings, Gandalf uses several staves to perform magical acts. Still, many have wondered on forums like the Tolkien Forum and Reddit if Gandalf would be unable to cast without a staff. While there is no direct answer in J. R. R. Tolkien's books or The Silmarillion, fans can assume that the staves possess a bit of magic but primarily act as amplifiers based on the lore. They focus the wizard’s powers, and each wizard -- from Gandalf to Saruman to Radagast -- gets one.
While the evidence behind this is a bit convoluted, Lord of the Rings fans know that Gandalf is a Maia -- an angelic-like being with innate magical abilities. Gandalf uses his staff’s capabilities to enhance his own when performing magic, but it isn’t required. Audiences see Gandalf set off fireworks on his way into Bilbo’s birthday party while his staff rests behind him. However, in his fight against the Balrog of Moria, Gandalf uses it quite a bit, and he even loses it due to the terrible battle. When Gandalf returns after the Balrog encounter, he comes back as Gandalf the White, complete with new abilities and new staff.
After, Gandalf visits the cursed Théoden where Gríma Wormtongue commands the guards to take the party’s weapons. Still, Gandalf manages to keep his staff, claiming that it’s merely a walking stick. It infuriates Wormtongue, who screams out, “I told you to take the wizard’s staff!” The anger and fear make it seem like Gandalf would be less powerful without it and a big threat with it. This theory is supported in The Lord of the Rings films and implies that staffs work much the way the arcane focuses do in Dungeons & Dragons.
However, Tolkien didn’t write anything specific about the staff’s powers or lack thereof, only that Gandalf -- and the other wizards -- had one. Most of what fans know about them, including how they look, is based on the films. Peter Jackson and his crew brought the magical items to life, even including the fantastic little notch for Gandalf's pipe.
Based on this information and the fact that Gandalf is reincarnated with a new staff, it seems safe to assume that a wizard’s staff is a part of him in a way. It allows Gandalf to channel magic stronger and more precisely. Gandalf the White's staff even matches his new aesthetic.
He also takes on a mortal form when roaming Middle-earth. As such, that form could affect his Maiar abilities to call on the magic of nature, making the staff more of a necessity. It makes sense that big “spells” would require a little extra oomph to pull off. A wizard’s staff provides that boost, making it a bit magical itself. But no typical mortal would be able to use it to do magic -- except for the wizard it belongs to.