Chemically, the combination of ammonia (NH3) and hydrogen peroxide (H2O2) with hair results in the production of a number of products. Most commonly water (H20) and oxygen (O2) will be produced as hair shafts are opened up and their pigments oxidised. It is claimed (without noting evidence) that some hydrazine (N2H4) will be produced, a toxic chemical. Since the reaction is exothermic, releasing heat energy, care should be taken when carrying it out in the presence of skin.
A combination of ammonia and hydrogen peroxide is often used in the process of bleaching hair. Hydrogen peroxide has the necessary properties to remove the color from hair - it oxidizes one of hair’s melanin pigments to a colorless substance. This results in the hair becoming lighter. Done time and time again, bleaching can lead to hair becoming a very light platinum blonde color. Bleaching is not successful if done on hair that is too dark to begin with, because one (orange) hair pigment resists oxidation - thus dark hair will usually turn an undesired orange color. You should mainly consider bleaching your hair if it is naturally (dark) blonde, and you simply want a lighter shade.
Mixing ammonia with hydrogen peroxide is common in commercial products, and often done elsewhere to bleach hair quickly and cheaply. However, it is not recommended by hair professionals (those who don't understand chemistry but want your cash), and can cause extensive damage to hair (even causing it to fall out). Done by someone ignorant and inexperienced, it is likely to go wrong. It could be worth the extra money to buy reputable hair bleach - which still benefits from an experienced hairdresser to monitor the bleaching process. Even better, spend a lot and get your hair bleached at a salon. Using home made mixtures of ammonia and hydrogen peroxide could either save money, or result in a hair disaster.