While I will speak a little bit to the history of Alsace-Lorraine prior to the Franco-Prussian war, the region's importance was really due to its iron and coal deposits during the industrialization of France and the newly-formed Germany, particularly in the period right before the First World War.

After the fall of the Western Roman Empire, in which both Alsace and Lorraine were part of Gaul, they fell under the control of invading German tribes, and were later ruled by the Franks until 870. At this point, Alsace and Lorraine took on separate histories, with Lorraine becoming an independent duchy in Germany and Alsace being incorporated into a duchy with Suabia. During this period, both duchies were predominantly German speaking.

Alsace would remain nominally under German rule until the end of the Thirty Years war, where it was annexed by France. Lorraine was later incorporated into France in 1766 through a series of deaths and inheritances. It's worth noting that both Alsace and Lorraine would remain culturally German until the French Revolution, at which point their citizen's service in the French military and fascination with the Revolution's political ideals caused a shift in the region's identity towards France.

So, just to recap, Alsace and Lorraine had spent nearly a millennium under German rule and identifying themselves as German, but had become pretty much fully French by the 1870's. So, this begs the question: why did Germany want Alsace and Lorraine back after the Franco-Prussian War?

Well, initially Germany mainly wanted Alsace-Lorraine to act as a buffer zone in the event of any future wars with France. The area contains the Vosges Mountains, which would be much more defensible than the Rhine River if the French ever attempted to invade. Bismarck was actually reluctant to take Alsace-Lorraine, but German general Helmuth von Moltke, whose nephew of the same name would later serve as a general in WWI, insisted that Germany annex the region for defensive purposes. Also, Germany still recognized that the people living in Alsace-Lorraine had been German for centuries, and there were people who still saw the region as rightfully German and felt a desire to reclaim it. It is worth noting that both Alsace and Lorraine did not want to be annexed, and left France against their will.

However, in the following years it became clear that the real value of Alsace-Lorraine wasn't the Vosges Mountains: it was the minerals buried within them. The iron deposits of Alsace-Lorraine were the second largest discovered deposits in the world in 1918. During WWI, there were 2,800 million tons of iron ore in Germany. Lorraine alone accounted for 2,000 million of those tons. Once the dephosphorizing process was discovered prior to WWI, the value of these ore deposits became abundantly clear to both Germany and France. Add in a solid dose of French outrage at the loss of their provinces against both their government and their people's will, and this explains why control over Alsace-Lorraine was so hotly contested during the first half of the 20th century.

EDIT: Corrected a few typos and my mistaking Moltke the Younger for Moltke the Elder.

Sources: https://www.jstor.org/stable/22512?seq=1#page_scan_tab_contents

https://www.jstor.org/stable/25121684?seq=2#page_scan_tab_contents

The imperial provinces of Alsace and Lorraine were fought over for a variety of reasons. Initially the main benefit was their strategic location. Located on the Rhine river, they were vital channels of control for both commerce as well as military operations. Due to the cumbersome nature of supply wagons and the constant need to feed an army on the move, it was very difficult to move armies from one place to another without either access to a river to bring supplies by barge or an area that had not yet been sacked by raiding armies. This was most seen in the 30 Years War when both Protestant and Catholic armies more or less were forced to conduct their operations by logistical imperatives rather than the other way around. Given that the Rhine river not only was the artery of Germany and France but also the Netherlands it was a critical asset in conducting operations, none more so than for the Spanish and Austrian Habsburgs, Holy Roman Emperors.

Alongside Alsace and Lorraine lay an important land route known as the Spanish Road. Alsace, Lorraine, and the Netherlands used to be part of the Duchy of Burgundy. When the last Duke of Burgundy died without an heir, his lands were effectively partitioned between the French and the Habsburgs. The German areas were absorbed into the Holy Roman Empire proper, while the Netherlands were given to the Spanish Habsburgs. Due to emnity between France and Spain, the only way for the Spanish to send troops and reinforcements to the Netherlands was via this Spanish Road, a sophisticated set of supply dumps, magazines, marchable roads, and river access that happened to cross through Italy and Alsace. For the Spanish to intervene in the Dutch Revolt and later the 30 Years War, this was the only method. France, which had conducted its foreign policy for hundreds of years with the view that the Habsburgs sought to contain France, had a strong interest in weakening this containment in whatever ways it saw fit.

Eventually, through what amounted to a series of salami tactics, the French were able to finally annex Alsace and Lorraine via a combination of military successes and legal maneuvering. This allowed France to stabilize its border to the east with the natural barrier of the Rhine. However, they had to contend with rising German nationalism under Prussian domination, which encouraged vast irredentalist behavior, seeking to control all areas that were of Germanic descent, including Alsace and Lorraine. This eventually led to the Franco-Prussian War, whereby Alsace and Lorraine were given to Prussia and was later reorganized as the province of Elsass-Lothringen in the German Empire. The French, for their part, viewed these lands as critical for France not only for nationalist and defensive purposes but also economic. For the Rhine basin where Alsace, Lorraine, and the German Saarland lay was beds of iron and coal, which in the Industrial Age were critical strategic resources for industry (as they are the key requirements of steelmaking). Even today Alsace and Lorraine are some of the wealthiest parts of France, in no small part due to the steel and automotive industries that lay in this area.

Alsace and Lorraine proceeded to change hands a number of times after the Franco-Prussian War, most notably after World War I where France, its industry in tatters after many of its industrial regions were occupied by the Germans (such as Franche-Comte) demanded to be returned to it in exchange for peace, then later back to Germany after the Nazi invasion of France in 1941. With the end of World War II, it had been generally recognized that Alsace-Lorraine, for both political, nationalist, and economic reasons, had been thrown back and forth in a tug of war that if not dealt with would likely lead to a further continuation of the historic Franco-German emnity.

Part of the reason why the European Steel and Coal Community-the precursor to the modern European Union-existed was in part to alleviate these concerns. The idea was that the local economies of scale between French Alsace and Lorraine, and that of the German Saar and Ruhr, would be better off if the regions were able to cooperate rather than compete against each other. This allowed both nations to economically benefit from the region even though it was finally given back to France. In combination with efforts to mollify European irredentalism, this has managed to keep Alsace and Lorraine from changing hands since. However, the German influence in Alsace and Lorraine is still very strong, for many people in the area speak both French and German.

Sources:

Supplying War, from Wallenstein to Patton, Martin van Creveld
The Army of Flanders and the Spanish Road, Geoffrey Parker
The Franco-Prussian War, Michael Howard
Coal, Steel, and the Rebirth of Europe. John Gillingham