A colony is an area of land under loose or strict control by another state/country. It can be a place in which settlers from the state move, sometimes displacing native residents, or a place where a state claims some ownership or right to rule the people there. Like the American colonies under British control in the 1700s, many modern ones are found in what might be considered unincorporated areas, where the residents are subject to the laws of the country that claims the area, but don’t get to participate in the political process that creates these laws. This has led some colonies in modern times to seek independence from a controlling state so that they may self-govern and pass laws appropriate to their land, culture, and beliefs.
The US has two areas of land that can be considered colonies, and also commonwealths: Puerto Rico and Guam/Northern Mariana Islands. While in the past, such territories of the US, especially in the contiguous states, lobbied for full rights as states, not all citizens of Puerto Rico are interested in this. Some are, however, and do campaign for turning Puerto Rico into an actual state or an independent country, as opposed to a commonwealth.
Citizens in Puerto Rico abide by US federal laws, but don't get to vote to make or change laws on a federal level. They don't have representation via senators or House representatives, though they are subject to the laws of the US by agreement between the leaders of the Puerto Rican government and the US. The island does have its own republican government, but its relationship to the US is still in some senses colonial.
Another colony, held by the UK, is Gibraltar, which has been a British territory since the passage of the Treaty of Utrecht in the early 18th century. The leader of the country is Queen Elizabeth II, though again, Gibraltar has its own government. Unlike other such areas, Gibraltar is recognized as a state by the European Union, which is unusual. Further, Gibraltar does not use the name “colony” to describe its relationship to the UK and instead prefers to be called an “overseas territory.” It is still subject to laws in the UK.
There are other small territories and islands that have colonial relationship to countries. The number continues to fall as people in territories feel they have the right to be recognized as either part of a larger country or as an independent state. Many want full rights to participate in the voting or political process, or to be considered as wholly separate from the other country.
There can be benefits to the colonial relationship when a state is small. For instance, a disaster in Puerto Rico would probably mean that the US would quickly come to its aid and bring necessary funds for recovery. There can also be difficulties when the people who live there aren't truly considered citizens and have no representation, however.