Refer to figure.
Note: This seems quite complex for the PPL syllabus, but the PPL syllabus is unforunately quite vague. This knowledge will set you up incredibly well for the CPL or ATPL exams in future if you decide to do them.

Lateral stability is the measure of an aircraft's roll response to a sideslip (try not to confuse this with directional stability, which is an aircraft's yaw response to a sideslip). When a sideslip condition occurs, the oncoming airflow is not hitting the aircraft head on, instead it has some lateral component, hitting the aircraft on one side at an angle. A laterally stable aircraft will respond to this by rolling away from the sideslip, for instance, sideslipping to the right (air hitting the right hand side of the fuselage), the aircraft should naturally roll to the left to remove the sideslip condition.

The most notable ways of causing lateral stability is with dihedral. This is where the wings are connected at an upwards angle from the fuselage, and this means that in the event of a right sideslip, the right wing has a greater angle of attack than the left wing, causing a roll to the left. This is because the lift produced by the right wing is greater than the lift on the left wing, and therefore the aircraft is unbalanced around the longitudinal axes and will roll left. Other ways to cause this same (or similar effect) would be to give the wings a sweepback angle or use a high wing design. These all increase angle of attack on the "upwind" wing in slightly different ways.

The question about flaps isn't so complicated anymore. As flaps are located towards the wing root and never really towards the wing tip, the majority of the lift is produced close to the wing root when flaps are extended, which shortens the distance between the aircraft's roll axis (longitudinal axis) and the centre of lift of each wing. This means that the effect of asymmetric lift is reduced, as the moment arm of the asymmetric forces are reduced, so therefore the lateral stability is reduced slightly.