Accelerometer X/Y/Z "high events"
Manufacturers' Data sheets for devices are often supplemented by their Application Notes.

There are a bunch of application notes on the LIS3DH page under the "Design Resources" tab.

One of those is AN3308: LIS3DH: MEMS digital output motion sensor ultra low-power high performance 3-axis “nano” accelerometer

It describes the features of the device. For example, in Section "6.2 Threshold", it explains how to set an acceleration threshold for an acceleration-triggered event. SImilarly "6.3. Free-fall and wake-up interrupts" explains how to define the type of event the LIS3DH should trigger.

AFAICT, depending on the selected mode, the event could be triggered by either an acceleration exceeding a threshold, and so could be directions of movement, or when the device is orientated in a particular way.

Edit:
Based on:


  5 Interrupt generation
  The LIS3DH interrupts signal can behave as free-fall, wake-up, 6D and
  4D orientation detection, and click detection. Those signals can be
  driven to the two interrupt pins (INT1 and INT2).    
  
  6 Inertial interrupt
  The LIS3DH can provide two inertial interrupt
  signals and offers several possibilities to personalize those signals ...


My interpretation is interrupts are intended to wake up the 'driving' MCU.