'Peak' and 'off-peak' relate to the times of the day when energy demand across the network is high or low. For example, most households use hot water and appliances before and after work which creates a high energy demand in the morning and evening. 

Different tariffs apply to peak and off-peak times and are determined by the kind of meter (or meters) you have at your property. If you have an off-peak meter then it is often cheaper to run some appliances overnight rather than mornings and evenings.