It is important to always use some form of luggage tags when traveling to ensure that bags can be returned to the rightful owner if they become lost. Leather luggage tags are a more upscale option than the plastic versions that generally come with most suitcases. They are generally more durable and can often be monogrammed or otherwise customized to match the luggage. On the downside, leather luggage tags are much more expensive, and can easily be lost or stolen with a little bit of effort, so some people find it easier to just stick with the plastic versions.
The main advantages to using leather luggage tags is to give the luggage a more upscale appearance. People who purchase a nice set of designer or expensive luggage will often want tags to match. They can generally be purchased at the same time, and generally feature a leather backing and strap with a clear plastic front for a card with the owner's name and address to be displayed. The leather strap generally makes them more durable and less likely to be pulled off a suitcase if it is not handled carefully, which is a fairly common occurrence in airports.
For people who want to invest even more money in leather luggage tags, personalized versions are another choice. These can be monogrammed with an individual's initials, for example. These generally need to be ordered online, but they can make a particularly great gift. Brides and grooms will often order monogrammed luggage tags for groomsmen as a gift.
Of course, there are some downsides to using leather luggage tags as well. Some people are not comfortable using leather products, particularly those who follow a vegetarian or vegan diet. Others find the price prohibitive, particularly since luggage tags come free with any luggage purchase, and often these free versions will work just fine. It is much more annoying if expensive leather luggage tags get lost rather than free plastic types.
In addition, people are more likely to steal leather luggage tags off of suitcases. This might not be true for monogrammed ones, but plain ones could be taken. This would virtually never be an issue with plastic luggage tags. In general, leather luggage tags make a nice gift, a good purchase for frequent travelers whose luggage takes heavy abuse, or a pleasing accessory to designer luggage, but otherwise they are a completely optional purchase.