"Hefe" means yeast, "Weizen" means wheat. Hefeweizen is a top fermented, unfiltered, bottle conditioned wheat beer with a noticeable yeast sediment and a cloudy appearance. Wheat beers are also referred to as Weissbiers (white beers) because before the invention of pale lagers and pale ales, most beers were dark. Wheat beers were the exception as the wheat content lightened the colour of the beer.
Hefeweizens are usually quite sweet and fruity, with a full body. The typical hefeweizen taste, which distinguishes it from its Belgian wheat beer cousins is produced by the types of yeast used in Bavaria. There are often medicinal or clove flavours, produced by chemicals called phenols engendered by the yeast. Other chemicals produced by the yeast, called esters, produce bubble gum, banana and vanilla flavours. Esters are also used in sweets like pear drops or fruit gums. Hefeweizens are very lightly hopped so have little bitterness and harshness. The ratio of wheat to barley malt used is commonly around 50:50 but the wheat portion may rise to as much as 70%. With the exception of Gose, German wheat beer brewers don't add coriander or other botanicals and spices to their beer as Belgian brewers do.
Hefeweizen should be poured smoothly into a tilted, rinsed glass. Pause when there's about a quarter of the bottle left, swirl the bottle to lift the sediment, then pour the rest into the glass to give a big, fragrant head and release the yeast into the beer to give it its cloudy appearance. The glass should be like the Franziskaner glass shown on the right - tall and graceful, with a narrow base widening toward the top before narrowing slightly again.
I've never seen a German add a slice of lemon to a Weissbier but apparently some do. I think it ruins the taste of the beer and the acidity of the lemon kills the head. I can see the point of adding a wedge of lime to Corona because the taste of the beer is so vapid that the zest of the lime is a welcome reminder that your taste buds are still working, but decent beers shouldn't need a fruit garnish, in my humble opinion. However, I'm told that it is more common to add lemon slices to the filtered version of Weissbier: Kristallweizen.
Wheat beers were originally forbidden by the Reinheitsgebot (German beer purity law), that forbade the inclusion of anything but barley, hops and water (spontaneous fermentation was used instead of yeast). Some say the law was originally intended to save wheat for the baking of bread. Roger Protz  states that the Bavarian royal family held a monopoly over barley production and wished to prevent the use of other grains in beer from undermining their monopoly. All the while, the royal Wittelsbach gangsters were still enjoying wheat beers denied to the general population. The laws were relaxed to allow the Schneider brewery to brew wheat beers in 1850. Schneider Weisse is still one of the better examples of the type, and somewhat darker than most.
Weizenbock is a variation on the Hefeweizen style but brewed to a have stronger alcohol content as with Bock lagers - typically around 6.4%.