Teeny means very small — smaller than 'small', and said with warmth. It is an informal, playful word, the kind of thing adults say to children, or friends say to each other. You would not put it in a report. Its close relatives are 'tiny', 'teensy', 'itty-bitty', and the doubled form 'teeny-tiny', which is very common in speech even though it is technically saying the same thing twice. Two things worth knowing about how it is really used. First, it very often turns up in 'a teeny bit', which no longer means 'small' at all but 'slightly' — 'Could you move a teeny bit to the left?', 'I'm a teeny bit worried.' Here it is softening what you say, not measuring anything. Second, when people want to stress how small, they stretch the vowel: 'It was teeeeny.' Second, it is a friendly word, so it can quietly signal that you find the small thing cute — a teeny puppy, a teeny apartment. Call a person's salary teeny and you sound like you are teasing them. There is also an unrelated noun 'teeny', short for teenybopper, meaning a young teenage fan; it is dated now and you are unlikely to meet it, but it explains why the word sometimes appears in old writing about pop music.