An exoplanet is a planet orbiting a star other than the Sun. The first confirmations came in 1992, and thousands are now known, most of them found not by seeing the planet but by watching what it does to its star. The population that has turned up is nothing like the Solar System: the commonest planets found so far are larger than Earth and smaller than Neptune, a size our own system does not contain.
If a planet's orbit happens to pass across the face of its star from our line of sight, the star dims by a fraction of a percent for a few hours, and does it again every orbit. The depth of that dip gives the planet's size relative to the star, and the interval gives the period. It only works for the small share of systems aligned edge-on to us, which is why the method finds many planets and misses most.
A planet does not orbit its star so much as the two orbit their common centre of mass, so the star traces a small circle of its own. That motion shifts the star's spectral lines blue then red, once per orbit, and the size of the shift gives a minimum mass for the planet. Combined with a transit it gives the mass and radius of the same body, and therefore its density — the only route to knowing whether a planet is rock or gas. The speeds involved run from a few hundred metres a second for a hot Jupiter down to nine centimetres a second for an Earth twin — which is why no spectrograph has yet found one.
The number of known planets does not grow smoothly, because confirmation does not. A survey watches the same field for years, accumulates candidates, and then validates a batch of them in one pass — which puts a thousand planets into a single year and almost none into the year before it. Reading a chart of that as a rate of discovery would be reading the release calendar of one telescope.
The habitable zone is the band of orbits where a planet with the right atmosphere could hold liquid water on its surface. It is a statement about distance from a star and nothing else. A planet inside it may have no water, no atmosphere, or no surface at all, and moons well outside one can be liquid inside from tidal heating. Where a system has enough measured about it, each planet page draws the zone around its own star: Kepler-186 f is inside its red dwarf's, at two-fifths of the Earth's distance from the Sun, because the star is that much fainter.