Ballistic capture is a method of achieving orbit around a planet or moon - a spacecraft moving at a lower orbital velocity than the target celestial body is inserted into a similar orbit, allowing the planet or moon to move toward it and gravitationally snag it into orbit around the celestial body with no need for an insertion burn.
It was first used by the Japanese spacecraft Hiten in 1991 as a method to get to the Moon.
It is predicted to be
Hohmann transfer orbit
The conventional method is a Hohmann transfer orbit.
Low-energy transfer
Low energy transfer (LET) was proposed in 80s. The spacecraft is launched into a transfer orbit that places it ahead of the target planet's orbital path. As the planet approaches the spacecraft, the planet's gravity draws the craft into a high circular orbit eliminating the need for an insertion burn. This orbit is a temporary one, eventually the spacecraft would leave it again - but then it uses low power thrusters to get into a lower orbit. It can use the much more efficient ion thrusters at this stage as there is no need for a high level of thrust.
With some target orbits the total fuel is less than for Hohmann transfer. Hohmann transfer is more fuel efficient if you target an orbit closer to Mars, but can only be done at particular times. Ballistic capture has the advantage that you can use it at any time.
In 2014 LET was proposed as optimal maneuver for future Mars missions. It can be performed anytime, not only once per 26 months as in other maneuvers and does not involve dangerous and expensive (fuel cost) braking. The only disadvantage is longer duration (up to one year, instead of six months in case of Hohmann transfer) of LET.