Lactate levels refers to the amount of lactate and/or lactic acid in your blood. Lactic acid is produced by the lactic acid energy system and is quickly converted to lactate before being transported  to your liver where it is converted to glucose. During exercise lactate levels rise in proportion to the intensity of the training (as shown in the graph)

This graph depicts the changes in lactate levels as intensity increases. At lower intensities the aerobic energy system can manage the suplpy of energy, keeping lactate levels around 2 Mmoles/L. Once the Lactate Inflection Point is reached, however, lactate levels continue to rise until fatigue.

Lactate levels in the blood rise in response to the body using the lactic acid energy system, which is required for higher intensities of training (~85%+). This means that during lower intensities, there is a slight rise in the lactate levels, but this level (normally around 2 Millimoles/L) is maintained throughout the training, before returning to resting levels once training stops.

In contrast, anaerobic training, such as short interval training, causes much larger increases in lactate levels due to the use of higher intensities that specifically rely on the lactic acid energy system. A sample comparison can be seen in the table below, where the aerobic training is constant, while the anaerobic interval training continually rises in response to the repeated bouts of high intensity workloads. 

As training begins both aerobic and anaerobic training cause an increase in lactate levels, but there is a substantial difference in the levels. Aerobic trainng then maintains the lactate levels, while anaerobic training causes the levels to continually rise until training is ceased. Once stopped both lactate levels slowly return to resting levels.

The rise in lactate levels is caused by using the lactic acid energy system. The more the body relies on this system, the more lactate is produced, causing the rise in lactate levels in the blood. This means that at lower intensities lactate levels will not increase as much. So for example, if the interval is 10s work and 20s rest the lactate level may stay under 3 Millimoles per Litre.