BGS = Background Simulation.
The "tick" is when time when influence and state changes update roughly every 24 hours at the same time each day. The activity for that period is aggregated and applied as a change in influence for minor factions.
The update cycle (i.e. approx every 24 hours) worked correctly and consistently before 1.4, except for patch days. Since 1.4 in October last year the update cycle has been notoriously unstable and inconsistent on a weekly and often bi-weekly basis. There are dozens of player groups who are trying to support their minor factions but it's becoming impossible due to influence movements not occuring and player actions for the cycle being erased as a result.
Some of us plan activities based on these influence and state changes, e.g. fighting in a war, trading at a specific station, bounty hunting in a target system, supporting different factions through missions, or locations to sell exploration data for explorers returing home after a long journey. The locations and types of activities will change depending on the current influence levels and states in the system. Short, medium and long term plans are made for minor factions which constantly evolve and change as a result of our activities.
This all relies on regular and consistent influence changes which don't happen! Sorry for the longish post, I got carried away a bit

The BGS is one of the main reasons I've played elite since it launched in December 2014.