お名前を教えてください

This is a polite phrase used to ask someone for their name. 'お名前' (onamae) is a polite way to say 'name', with the honorific prefix 'お' (o). '教えて' (oshiete) is the te-form of the verb '教える' (oshieru), meaning 'to teach' or 'to tell'. 'ください' (kudasai) is a polite request form, meaning 'please give me' or 'please do for me'. The combination forms a polite request for someone to state their name.