A simile says one thing is like another. It is an overt, or open, comparison. You can recognise it by the fact that it uses a word like 'like' or 'as' when making the comparison. 'He is as good as gold', says the mother of her baby; or she might say, of the similarity between her twins, 'They are like two peas in a pod'. Her husband, rushing to get her to hospital, may have 'driven like a madman', but, after the birth, may have been 'as proud as a peacock' or 'as pleased as Punch'. (Similes - particularly conventional ones - can be pretty meaningless: AWE does not know why Punch should be so pleased; nor why - to use a North of England example - a 'brush' should be 'daft'. But people are often said to be 'daft as a brush'.)
There are also possibilities of expressing feelings as well as simply communicating an image. There are several clichéd similes, for example, for 'pride'. If we want to congratulate someone, we can say 'You must be as proud as a prince'. If we want to suggest that this is a bad pride, we say 'proud as Lucifer' (one of the names, in Christian mythology, for the devil). 'Proud as a peacock' is much more neutral; it is nearer a statement of fact, albeit one that is expressed in a way intended to be vivid.