Gandalf is supposed to be a great and powerful wizard, whose old age has given him wisdom and authority over most of those within Middle Earth. Gandalf is very wise, and he is who The Fellowship turns to when they have doubts and need answers. He can also cast spells and tricks of the mind. Gandalf used his hypnosis powers on a moth so it could send a message to the eagles, he used his staff as a light source several times, he used his powers and a spell to keep a door the Balrog was trying to open shut, and he even used his powers to preform an exorcist-like ritual on Théoden when Saruman had put an enchantment on his mind. But despite all this talk of magical abilities, Gandalf rarely uses his magic.
If Gandalf can use a spell to ward off Nazgûl and talk to any creature he wants, why is he not using his powers at all times (as much as he can) throughout the trilogy? Gandalf was able to take on a Balrog singlehandedly, keep it from being unleashed onto Middle Earth, and kill it. Surely that means he has more to offer the battle than some well-trained sword fighting. Well, in Tolkien's fantasy The Lord of the Rings world, "magic and wizards" are very different than they are in Harry Potter. In Tolkien's work, "wizard" really means "wise" as a wizard is really just an authoritative, wise figure. Also, "magic" can better be interpreted as "knowledge."
Unlike magic for the wizards of Harry Potter—who say a spell, wave a wand, and make colorful sparks fly—magic for the wizards of The Lord of the Rings looks more like ancient technology than anything supernatural or magical. Gandalf is a wizard, which in The Lord of the Rings means he is an angelic spirit known as a Maiar (a shape-shifting being of authority and power that has existed since the beginning of time). Because magic in LOTR is not like it is in traditional fantasy and acts more like very old knowledge, each wizard (or Maiar) has control (or the most knowledge of) one particular aspect of life. To make it easier to understand, one could look at magic like very old technology they must learn how to read and understand before it can be useful to them, and each wizard takes an interest in different "technology" or spells.
The magic of The Lord of the Rings is more mental than physical. There doesn't appear to be any sort of Avada Kedavra or "eat slugs" types of spells in Middle Earth, so even if Gandalf used more "magic," it still wouldn't be the type one would see in close combat. Different types of magic seen in LOTR include telepathy, illusion, illumination, deception, element/weather control, and to some extent control or domination over others. For Gandalf, his main powers seem to be those over light and illumination. Gandalf uses his staff just like it is some ancient alien technology where all he has to do is touch the staff's crystal a certain way for the technology to work (like a really cool flashlight/torch). And Gandalf also has an affinity for fireworks and probably is able to control the lights in some capacity to have better firework shows.
Even if Gandalf had more traditional fantasy powers, he would not be able to constantly cast spells. As shown with Saruman, using magic is very taxing and expends great energy, so it cannot be done freely. When Saruman speaks to Sauron using the Palantír, the audience can see Saruman in the next scene and how weak he is from activating the old technology of the ball of crystal. When Gandalf is trying to keep the Balrog from passing the bridge and opening a door into Middle Earth, viewers can see how much energy and strength Gandalf is using to keep the door shut. He is even almost killed due to energy expenditure, and he later does die atop the snow-covered mountain—not from any injuries received from the Balrog, but rather just from mental and physical energy usage.
Wizards in The Lord of the Rings use their vast and infinite knowledge to influence those of Middle Earth so that good may prevail over evil. Maiar spirits do not have permission to interfere directly with the affairs of Middle Earth. All they can do is give people a little nudge out of the door and provide wisdom and guidance. Because they have great powers and can have influence over the minds of those around them if they so choose, wizards (like Gandalf) would be able to control the decisions of others but at great cost in energy. And even then, it would be difficult (or rather impossible) to use such a power against an entire army of orcs, trolls, and goblins.