The main purpose of the ref attribute is to make the DOM element selectable by being the key in the parent $refs attribute.
For example your input element there, with ref="input", would expose its DOM node in its parent (here inside currency-input this), as this.$refs["input"] (or this.$refs.input).
See: https://v2.vuejs.org/v2/api/#ref
It has several use cases, even if it would be often better when possible to not manipulate the DOM directly. For example, a legitimate use case here is to put focus on this input: for that you can use this.$refs["input"].focus() in a method of the component…