What constitutes a "cycle" with regards to lithium-ion or similar batteries?

Generally, in discussions about batteries in the context of home storage, one cycle will refer to a battery being fully discharged to the greatest extent the integrated system it is a part of allows. Or if it is not part of a system and just a battery on its own, a full 100% discharge.

Generally small discharges are summed together and measured as the number of full discharges they equal. Using small amounts of power from a battery system during the day is not a problem for lithium battery systems and should result in little or no more deterioration than a sustained discharge.

To cut down on confusion, battery storage systems now generally warrant the total number of kilowatt-hours (kWh) of stored electricity used, expressed in Megawatt-hours (MWh).

1MWh = 1000kWh

For example a battery may be warranted for 3 MWh. That's 3,000 kWh. If you cycles the battery once a day that would be just over 8 years.