The Tarot court cards are often those that we find hardest to interpret. A 'traditional divinatory' approach would often limit them to signifying people with specific physical appearances, based on the suit. Since modern Tarot is much more focused on self-development than prediction, "you will meet a dark-haired, dark-eyed man" is rather less than helpful.
There are now various established systems for reading court cards, and most readers will use a combination, selecting the most appropriate interpretation for each reading specifically. Many of these use some kind of system of meaning for the court position (i.e. there is a meaning for the 'kingness' of a card), which you combine with the suit drawn. This can be based on qualities associated with the character of a King (e.g. mature masculinity), Queen (mature femininity), Knight (relative immaturity - a teenage or adolescent kind of energy) or a Page (childhood innocence). Some readers will also assign an element to each of the four courts, and read each drawn court card as an interaction between the court position's energy and the energy of the suit (e.g. the King of Pentacles could be seen as Air of Earth).
I find that the system I use depends more on the deck than on anything else. Some decks change the court labels for different people (e.g. Knights and Pages become Princes and Princesses in the Thoth deck) or rename them entirely - the Songs for the Journey Home deck has (element name) Resolving, Creating, Awakening and Innocence for the four stages. Some of the more RWS (Rider-Waite-Smith) style decks will depict quite traditional characters on the court cards and will more often lend themselves to interpretation as a person.
If you read tarot and would like some help with courts, I'd recommend you follow Alison Cross's This Game of Thrones blog, which focuses specifically on the courts. A good book on the topic is Little and Greer's Understanding the Tarot Court, which goes into a lot of detail on various ways on approaching it.