The Made With Love blog has posted a great introduction to version handling in Composer today. They focus in on two characters that can be confusing if you're not exactly sure what they mean - the carat (^) and tilde (~).

A dependency that uses semantic versioning allows you to predict wether it is still going to work or not when you upgrade it to a new version. Basically when the x in a x.y.z version number changes, you might need to do some changes to be able to work with this new version without problems. [...] Depending on your dependency manager you can define version constraints using wildcards (*), comparators like <=, logical operators (, often means AND and | means OR), etc. [...] There are also some syntactic sugar operators like ~ (tilde) and ^ (caret)

They include some examples of both characters in use defining the required install versions, showing how one allows for approximate matches and the version ranges they apply to.