All-purpose flour is used most commonly. It is a mixture of soft and hard wheats so its texture is in the mid-range between soft (as in fluffy cakes) and coarse (as in whole grain breads.) There are two kinds of all-purpose flour ~ bleached and unbleached. The latter contains more nutrients and protein and has a better taste. All-purpose flour is normally used for breads, as well as puddings which have a more weighty consistency than cakes. Some examples are Danishes, scones and biscuits. 'All-purpose' means just what it says; the flour is adaptable to a huge variety of recipes.
Bread flour is made from hard wheat. It is courser in texture than all-purpose flour and contains more nutrients. It is used for making denser breads like Ciabatta. Cake flour is made from soft wheat. It is usually bleached, which helps it to absorb sugar and also contributes to the cake's fluffiness. It is used in light, fluffy cakes, like sponge.
Using the wrong kind of flour can result in a 'flop,' but luckily, recipes usually make clear what kind of flour to use.