Both Nickel and Azo (Azocolorant) are toxic/ harmful to human.
Nickel = 鎳. 是化學元素之一,化學符號為Ni,原子序數為28,具磁性,屬過渡金屬。
http://zh.wikipedia.org/w/index.php?title=%E9%8E%B3&variant=zh-hk
http://en.wikipedia.org/wiki/Nickel
Why need Nickel-free:
Exposure to nickel metal and soluble compounds should not exceed 0.05 mg/cm³ in nickel equivalents per 40-hour work week. Nickel sulfide fume and dust is believed to be carcinogenic, and various other nickel compounds may be as well
Nickel is normally found on metalwares, jewelries, glasses frames, etc.
Jewelries, glasses frames export to European Countries are regulated by EU Directive 94/27/EC (Nickel Release).
Nickel can cause allergy to some certain people:
http://www.aocd.org/skin/dermatologic_diseases/nickel_allergy.html
Azo is a sometimes included in Dye (染料).
http://en.wikipedia.org/wiki/Azo_compound
Azo dyes are often used in the colouring process of several textiles and leather products. Relatively recently it has been recognised that some azo colouring agents may form amines (breakdown products), which have carcinogenic and mutagenic properties.
The European Union published a Directive (2002/61/EC), based on 76/769/EEC, to restrict the marketing and use of certain dangerous substances and preparations (azocolourants) in textile and leather products. The legislation is relevant for all products made of textile and leather or in which textile and leather is used and which come into direct and prolonged contact with the skin and mouth. These include producers of textiles and garments, leather goods, shoes, toys, furniture, decorative articles, jewellery and accessories.
Nickel-free and Azo-free are basically just, goods that do not include these element/chemical.
Normally, these two requirements are needed most for goods export to European countires. The goods need to be tested and pass by relavant Laboratories before being shipped. These Labs include Intertek, Bureau Veritas, SGS, etc.
You can search for EU Directives (by Legislation number is fine) on:
http://eur-lex.europa.eu/RECH_mot.do