There are essentially three types of island colony - those that have an intrinsic strategic advantage due to geography, those that can produce a decent amount of goods, and those that are solely useful for prestige.
The first type include Malta, Guam, and to a lesser extent the Falkland Islands. These islands are placed on major shipping routes. Naval forces operating from them can interdict shipping along these routes. They can also serve as replenishment stations for forces moving along such routes. Other islands can provide bases for forces operating against a hostile coastline, in blockade or in amphibious operations. Examples of this would include Minorca or Bermuda, both of which were used by the British for this in the late 1700s and early 1800s. Islands like New Britain, which aren't necessarily well placed, but have excellent harbours, would also fall into this category.
Other islands can have useful economic output. The Caribbean islands, Sri Lanka, or the islands of Indonesia all fall into this category. These islands have some combination of a large available workforce, a good climate for growing cash crops, or abundant natural resources. The Indonesian islands were initially a major source of spices, while in the 20th Century oil was discovered there. Sri Lanka also produced spices, but mainly exported tea and coffee during the period of British rule. The Caribbean islands were excellent for producing sugar, leading to the Atlantic slave trade.
Finally, some colonies had no intrinsic strategic advantage to the nation that held them. They were merely there because it was prestigious to have a colony. This would include most of the German Pacific colonies - the Caroline Islands, or Palau, had very little strategic use to Germany. They were colonised because public opinion in Germany was in favour of colonisation.