An Orbit is the trajectory of an object moving in a circular, elliptical, or hyperbolic path around a bigger object, attracted by its gravity. Mars and other planets are orbiting the Sun in an elliptical trajectory. Mars is orbited by two moons: Phobos and Deimos. The science of Orbits is Orbital mechanics, a subset of Astronautics. Space vehicles with engines can change orbits through thrust, or have continuous thrust orbits and therefore affect their orbital mechanics in various ways to achieve transfer form one planet to another.
Low Earth Orbit is the minimum height (160 km) and velocity (8 km/s) that an object needs to stay in orbit round Earth. This orbit is the easiest to reach with currently available rocketry. It might be used to assemble a large spaceship from smaller parts that are lifted separately from Earth. LEO is subject to drag from the Earth's atmosphere and vehicles in LEO need to be booster periodically to avoid orbital decay and re-entry. LEO is actually a range, extending up to 2000 km above the Earth
Low Mars orbit is similar to Low Earth Orbit. Although Martian atmosphere is less dense, with a lower gravity it extends practically as far.
An areostationary orbit is the same as a geostationary orbit, but around Mars (from the greek name of Mars, Ares). This orbit is 17 000 km above the Martian surface, considerably less than Earth's geostationary orbit at 35 700 km ( 24 000 km above Earth's surface).
Hohmann transfer orbit
In orbital mechanics, the Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. In general a Hohmann transfer orbit uses the lowest possible amount of energy in traveling between two objects orbiting at these radii, and so is used to send the maximum amount of mission payload with the fixed amount of energy that can be imparted by a particular rocket. Non-Hohmann transfer paths may have other advantages for a particular mission such as shorter transfer times, but will necessarily require a reduction in payload mass and/or use of a more powerful rocket.
A forced orbit is any powered orbit that depends on a vehicle engine or aerobraking to achieve orbital transfer between two bodies. They are used to reduce transfer times between planets and other bodies. They require more powerful engines than low energy trajectories. The NASA Ames Trajectory browserprovides a handy way of determining rapid orbits from Earth to Mars.