I'm not a rocket scientist, but I would say likely that's when the launch window opened, or it was inside the window to be able to get the craft on the right trajectory to Mars. Launch windows take into account where the target's orbit is (in this case Mars) and where Earth is inside that window. In this case, the launch window was likely quite large due to Mars' orbit being quite a distance from Earth (and quite stable) which leaves quite a bit of time for correction burns in case the rocket is off course at all.
The first relevant thing is indeed the orbital position of Mars in relation to Earth. For simple Hohmann transfers, launch windows to Mars open every 26 months or so, and they last several days. In this case, ExoMars launch could have been delayed until March 25 had any issues prevented the launch today.
The second timescale has to do with Earth's rotation. Even though most interplanetary spacecraft, including the ExoMars probe, are launched into a temporary parking orbit before injection to transplanetary trajectory, that orbit needs to have the right shape and inclination to make the injection burn feasible from the fuel economy point of view. Orbital plane changes are particularly expensive. Thus, the daily launch window may only last a minute or so when the launch site intersects the plane of the ecliptic.
