A terrestrial planet is an Earth-like planet, consisting mostly of rock (as opposed to gas or ice). The other terrestrial planets in the Solar System are Mercury, Venus, Mars and the dwarf planet Ceres.
Outside the Solar System, Earth-like planets might harbor life as we know it. They will be in a temperature range between 50 and 450 degrees Kelvin. They will have a good deal of water or methane (some think ammonia based life is possible).
Planetary scientists have constructed a graph of where an Earth-like planet might exist. On the Y-axis is the size of the star; the X-axis is the distance from the star. On a star the size of the Sun, the Earth-like orbital zone is just before Venus to just after Mars. Any closer than Venus and the planet would be too hot. Any further than Mars and the planet would be too cold. If the star is smaller than the Sun, then this zone-of-life is closer to the star; if the star is larger then the zone moves out some. If the star is less than about 0.5 times the size of the Sun, or more than 3 times as large, there may not be any zone-of-life.
One interesting exception to the zone-of-life rule is Saturn's moon Titan. Titan is about 70 degrees Kelvin and has an atmosphere of methane. The methane could be left over from the formation of Titan, but streaming solar particles from the Sun at that distance give methane a half life of 10**6 years. Since Titan is assumed to be much older than that, there must be a process to either protect the methane or to regenerate it.
Detect a Planet
There are several ways to detect planets that might exist orbiting other stars.
1. Observe the wobble in a star. If a planet orbits the star then there will be a slight movement in the star's position as the planet's gravity tugs at it. From the amount of observed movement, the ratio of the mass of the two can be inferred.
2. Observe a periodic change in the Doppler shift of the light from the star. This periodic shift would also indicate a wobble caused by an orbiting planet. The shift occur as the star is alternately moving towards the Earth and away from the Earth.
3. Observe a periodic change in the brightness of the star. There will be a slight change in brightness when the planet transits across the face of the star. A detectable change will only occur if the orbital plane of the planet is within, say, 10 degrees of edge on to us. The size of the planet can be inferred by the amount the brightness decreases. For example, an Earth size planet transiting a Sun size star would decrease the brightness by about 0.001%. Detection is only possible by observing many transits and adding up the values over time; after enough time the signal to noise ratio will be high enough for the planet to be detected.