Defining the Exoplanet
TL;DR: An exoplanet is any planet orbiting a star outside our solar system, and they are incredibly difficult to see directly because they are tiny, dim, and drowned out by the blinding light of their parent stars.

The Definition of an Exoplanet
For most of human history, we looked at the night sky and assumed our solar system was the only one of its kind. We knew of the eight planets orbiting our Sun, but the vast, dark spaces between the stars remained a mystery. An is exactly what it sounds like: a world beyond our neighborhood.
To be classified as a planet, an object must meet three criteria: it must orbit a star, it must be massive enough for its own gravity to pull it into a spherical shape, and it must have cleared its orbital neighborhood of other debris. When we find these worlds, we are essentially looking for smaller, dark objects caught in the gravitational grip of a much larger, brighter object. They come in all varieties, from massive, gaseous giants that dwarf Jupiter to small, rocky worlds that might resemble Earth. The challenge, however, is that they are almost never found sitting alone in the dark.
The Problem of Contrast and Distance
Imagine trying to spot a firefly crawling on the edge of a powerful stadium floodlight from a distance of several miles. The firefly is the exoplanet, and the floodlight is the star. Because stars are unimaginably bright and planets are relatively cool and dark, the light from the star completely washes out the faint reflection of the planet. Even our most powerful telescopes struggle to separate the two.
Furthermore, the distances involved are staggering. The closest star system to us, Alpha Centauri, is about $4.37$ light-years away. That is roughly meters. At that distance, the angular separation between a star and its planet is so microscopic that it requires space-based optics with immense precision just to keep the star's glare from bleeding into the planet's position. We aren't just looking for a needle in a haystack; we are looking for a microscopic speck of dust caught in the beam of a lighthouse from across the ocean.
Why We Can't Just Use a Camera
Direct imaging—taking a literal picture of a planet—is the "holy grail" of astronomy, but it is rarely the way we first discover these worlds. Direct imaging requires the planet to be very large, very hot (so it glows in infrared), and very far from its star. Most exoplanets do not fit this profile. Instead, we rely on indirect methods that look for the influence the planet has on its star.
Think of it like a dance. A planet doesn't just orbit a star; both bodies orbit their common center of mass. This causes the star to "wobble" slightly or dim periodically as the planet passes in front of it. By measuring these subtle changes in the star's light or motion, we can confirm a planet's existence without ever seeing the planet itself. This requires us to be masters of data analysis, turning patterns in light curves into maps of distant solar systems. We are not looking at the planets; we are looking at the fingerprints they leave behind on the light of their host stars.
Exoplanets are discovered by observing the subtle gravitational or light-blocking effects they exert on their host stars, rather than by taking direct photographs of the planets themselves.
Now that we know what we are hunting, it is time to look at the specific footprints these worlds leave behind in the light of the stars they orbit.