奶奶

奶奶 (nǎinai) is the everyday word for 'paternal grandmother' — your father's mother. Chinese family terms are far more specific than English ones: the mother's mother is a completely different word, 外婆 (wàipó) or 姥姥 (lǎolao). The 外 ('outside') prefix on maternal relatives reflects the traditional view that married daughters joined the husband's family, so the mother's side became 'outside' the patrilineal line.

The doubled form 奶奶 (rather than just 奶) is typical of intimate family terms in Chinese — see also 爸爸, 妈妈, 哥哥. 奶奶 is also used as a respectful form of address for any elderly woman, similar to how English speakers might call any older woman 'grandma' (though in Chinese this is more universal). Note that 奶 by itself means 'milk' (牛奶 'cow milk') — context is what tells you which meaning is in play.