Talk to any fly angler and they will tell you the most consistent technique for catching trout is by nymphing. This technique is successful because trout take the majority of their food from deep in the water column where nymphs are most abundant. To be a successful nymph angler you need to get your nymph down to the stream bottom and that is where bead headed flies come into The most common type of bead used on nymphs is a brass bead. Tungsten beads are becoming more and more popular these days and have a few advantages over brass in some situations. Glass beads are also used but more as a component rather than as a weight source. I'm pretty much of a traditionalist when it comes to nymph patterns and usually stick with the Prince, Pheasant Tail and Hare's Ear.
Tungsten is about 40% heavier than brass so equivalent sized patterns will have the scales tipping on the side of tungsten. This becomes very important when you are fishing in fast water, deep water or you want the nymph to really stay tight to the stream bottom. The key here is being able to control the fly better. Let's say you have identified a nice fish holding in a trough in about four feet of water and the current is fairly brisk. You have a #12 brass bead head Prince tied on and you figure that you will need to cast about twenty feet upstream of the lie to get the right drift. After you make your cast you still need to make several mends to get the fly down and you still need to keep control of the line. By using a heavier tungsten bead fly you will probably only need to make the cast ten to fifteen feet above your target because the fly will descend quicker getting to the proper depth and drift. Because you have less line on or in the water you automatically have more control of the fly.
A similar situation would be that you need a #14 Pheasant Tail to tumble around the gravel and rocks right on the bottom because that is where the fish are eating and they aren't taking anything any larger than a #14. Unfortunately your #14 brass bead fly doesn't get you to the bottom because the current is too fast. A #10 brass bead fly gets you to the bottom but the trout don't even give it a sniff because it is too big. The extra weight of the #14 tungsten fly gets you right to the bottom and with the size of fly the fish are feeding on. Bingo.
What makes fly fishing so exciting is that it is constant experimentation and when you get all the factors right you are rewarded with a fish on the line. Dialing into the right fly weight is one of those factors that can turn your success rate around in a hurry. So, if you don't have an assortment of tungsten beaded flies, add a few patterns to your fly box and see what success they can bring to you.