"Negelvasser" has it's source in the Yiddish Language. It is the washing cup that is used to remove the impurities that have come upon the hands of a Jew through contact with forbidden objects or through the impurity that rests upon one's hands upon awaking from sleep (that is longer than 20 minutes), because sleep is akin to 1/60th of death according to Jewish Law.
The cup has to be able to carry a certain amount of water, and it should have two handles.
There are two ways to use the negelvasser, and that depends on your purpose.
The first way is the general and most common use of the cup, which is to remove impurities from the hands that have come upon them. This first way of washing is done after waking up from a state of sleep, after going to the bathroom, taking a shower, engaging in sexual relations, or any other appropriate use. The prevailing custom is to pour water over the right hand first, and then to pour water over the left. While halacha (Jewish Law) requires a minimum of two times for each hand, according to Kabbalah, and Chassidic (including Chabad) customs, one should wash each hand THREE times.
The second way to use the negelvasser is when you intend to have a meal, which means you wash your hands and then you say the "...al netilas yadayim" beracha (blessing) over your hands. You then proceed to take a piece of bread (or during the Sabbath, two full challas or two challah rolls), put them together, and say the "...hamotzi lechem min ha'aretz" beracha (blessing) over the meal you are about to eat, and then you dip the bread into salt three times (some have the custom to pour the salt over the bread, however the dipping is more proper according to Kaballah.) The way to wash here is to first pour water three (or two, minimum) over the right hand, and then to pour water over the left hand three (or two) times, and then say the beracha. Keep in mind, when saying this kind of beracha and taking part in this kind of meal, you are obligated to also say the after-berachas for the meal, also called in Yiddish, "bentching".