Living indicators are species that are sensitive to changes in the environment. For example air pollution can be monitored by looking at lichen, which are sensitive to sulphur dioxide in the air. The number of lichen at a particular location indicates how clear the air is. Similarly, mayfly larvae are good indicators for water pollution because they're sensitive to the concentration of dissolved oxygen in water.
Non-living indicators are things like satellites which can measure the temperature of the sea surface, weather stations that measure atmospheric temperature, rain gauges to measure rainfall, and dissolved oxygen meters to measure concentration of dissolved oxygen in water.