Unsalted Butter is butter with no salt added. It will therefore, in theory, have only one ingredient: cream. This results in a shorter shelf-life then salted butter. 
Unsalted Butter has to be fresh, or you know right away if it’s off; there’s no salt to mask off-tastes or extend its shelf life.
Those used to salted butter find Unsalted Butter bland. Those used to Unsalted Butter maintain that the subtle sweetness of the butter gets replaced by the sharpness of the salt. Consequently, many Unsalted Butter lovers dismiss salted butter. In return, salted butter lovers say that Unsalted Butter lovers are either snobs, or are health fanatics over a little salt. But Unsalted Butter lovers say that they prefer the choice of whether they are also consuming salt or not, and that many of them are in fact salt lovers: they just prefer to add their own choice of salt at the table.
In some places, Unsalted Butter is the same price as salted butter; in other places, salted is less, or salted is more.
 Various jurisdictions, however, allow the addition of a colouring ingredient such as annatto, which they also allow the butter makers not to count as an ingredient.
Unsalted, cultured butter has a marginally higher smoke point than salted butter, making it marginally better for frying.
Some recipe writers insist you use Unsalted Butter, and then call for you add to salt further down in the list of ingredients. Some find this ironic; in their defence, recipe writers say they are doing this to give more control over the salt content in a recipe, as the salt content can vary wildly (see Substitutes below.)
When using Unsalted Butter in a recipe that calls for salted butter, per 1/4 pound (1/2 cup / 125 g) of salted butter called for, assume that you need to add between 3/4 and 1 teaspoon of salt along with the Unsalted Butter. But because there is no standard for how much salt is in salted butter, it really depends on the brand called for (if specified), and your personal taste. Some brands only have the equivalent of 1/8 to 1/4 teaspoon of salt per 1/4 pound (1/2 cup / 125 g) of butter.