When something is polarised its ends are oppositely charged. So, depolarisation is when the difference is balanced, the ends no longer have different charges.
For example in neural stimulation, a neurone can become depolarised when the cells resting membrane potential (RMP) (-75 mV) becomes more positive (+40 mV). This occurs when the cell is stimulated via an action potential; the membrane contains voltage-gated sodium channels that become more permeable to sodium ions allowing them to diffuse out of the cell down their concentration gradient, making the overall charge more negative relative to the outside.
When a membrane becomes depolarised this can trigger an action potential. This can be defined as a rise in the membrane potential to +55 mV which is considered the threshold voltage. This threshold voltage is triggered when a stimulus is large enough to generate a high frequency of action potentials. When the membrane potential then falls back to the RMP this is reffered to as repolarisation. Typically, repolarisation results in hyperpolarisation of the membrane (a potential lower than the RMP) as potassium channels take a longer time to close than sodium channels.