Gibraltar is a strategically important piece of land. It controls the entrance to the Mediterranean, and since the Suez canal did not exist yet, the strait of Gibraltar was the only the way to get out of the Mediterranean sea. Several British monarchs and leaders like Oliver Cromwell had seen the value in Gibraltar, and had considered capturing the strip of land and converting it into a major naval base. The British gained control of the territory in the war of Spanish succession and have held it since. The origins of the war are complicated, the simplified version is that the French wanted to put their own candidate on the throne of Spain, and the rest of Europe, fearing a Franco-Spanish union backed a rival claimant to the throne.

A major goal for Britain in the war was the elimination of France and Spain's naval power, as those two nations were among the chief threats to Great Britain, and its empire in North America. The problem for Britain was that a significant portion of the Franco-Spanish fleet was located in the Mediterranean sea, far away from any British naval base. The British needed a port from which they could rearm and repair ships and then send them straight into the Mediterranean, to this end the British sent a force to attack Gibraltar. It was taken relatively easily in early August of 1704 by a combined Anglo-Dutch fleet that had set sail from allied Portugal, but it was besieged by the French and Spanish forces soon after its capture, remarkably the British just barely held onto Gibraltar and it was officially given to the British in the Treaty of Urtech in 1713.

The British attached great importance to the island, and that's why they still hold onto it today. Gibraltar was seen as one of the key areas that the British felt they needed to hold onto at all costs, because it allowed the British to control access into the Mediterranean, it also had great important as a military installation. The British stationed significant naval forces in Gibraltar and it gave them a base to harass and attack shipping or enemy ships trying to pass through the Mediterranean. Coupled with the British control of Malta made the British one of the dominant naval forces in the Mediterranean, despite only having a bit of land on the sea. Finally it was also a potent prestige symbol. The British public felt that to give up Gibraltar, would be a serious blow to British pride and prestige. It was described as:

a symbol of British naval power and symbol of the empire which has been built and, more than the British lion or even John Bull himself, has come to represent Britain's power and prestige across the world."

A good source would be "The Rise and fall of the British Empire" by Lawrence James and for a book on the modern issue of Gibraltar, I would recommend "Britain, Spain and Gibraltar 1945-1990: The Eternal Triangle" by R.H.Haig

All right, let's set the stage:

Charles II of Spain dies at the end of the year 1700. The only legitimate ruler of Spain would be the son of Louis XIV of France, a well known bad-ass and also arguably the most powerful ruler of France, Which meant that the King of France would also be the ruler of Spain. Charles knew this, and declared Philip, Duke of Anjou as his heir, who despite being Louis XIV's grandson, would not inherit the french throne.

But Louis XIV, as we discussed earlier, is a bad-ass and wanted his son to rule over both Spain and France and He was determined to see it through, but the rest of Europe was equally determined not to see it through because a united French and Spanish monarchy would be too powerful, Hence the incredibly complicated outbreak of the War of Spanish Succession.

So Parts of Spain, Portugal and France go to war with basically the rest of Europe (Britain, Netherlands, The holy Roman Empire, Austria and a bunch of other minor states). Britain and The Netherlands are the main naval powers at the time, and together they team up and take the port of Vigo, which is in Northwest Spain, directly above Portugal. The battle was an overwhelming military victory for the Allies against Spain and France, but otherwise unimportant strategically. Its main importance was that it boosted morale and it convinced the King of Portugal to switch sides against Louis XIV. With the addition of Portugal into the alliance, The allied fleets could base at Lisbon.

Lisbon is key because it allows the allies to launch an attack on the straits of Gibraltar, which would allow the allies to control the Mediterranean and to attack France from the North and the South. The allies had already attacked the port of Cadiz, near Gibraltar on the Southern side of Spain, but was unsuccessful. Now based at Lisbon, the Allied fleet sailed around the Mediterranean for a bit before concluding to attack Gibraltar for their base in the Mediterranean and to please their kings which were itchy for another morale boost.

Gibraltar was not defended as well as Cadiz, mostly because the terrain was rough and the amount it would cost to build and keep a garrison there, but it was still defended pretty well. The Alliance seized the Rock, and repelled the French counter attack. The British supplied the troops to maintain the garrison on the rock, and stayed there for the rest of the war. When the war turned against Britain, they signed the Treaty of Utrecht where they left the war but were given Gibraltar, a key asset for Mediterranean trade. The British fought off some Spanish attempts to retake the rock, and its been theirs ever since