Standard mindfulness practice involves observing various aspects of sensory experience as they arise moment by moment without interfering. Stated differently, it is a process of observing how matters unfold without grasping or resisting the natural flow. We might call this working with spontaneous sensory activation. But there is a common practice within many contemplative traditions, including mindfulness, of intentionally activating certain sensory experiences and then working with them in some systematic way. We could call this family of methods working with Intentional sensory activation.
Intentional sensory activation can be accomplished either subjectively or objectively. Subjective intentional activation involves calling up thoughts, either visual, verbal, or both, chosen in anticipation of those thoughts eliciting an emotional response. We call this subjective practice "evoking". Objective intentional activation involves exposure to outside visual or auditory stimuli, or through somatic stimulation. This we call this intentional activation using objective stimuli "triggering". The emotions evoked or triggered can be of any nature, pleasant or unpleasant, mild or intense.
A well-known practice evoking "positive" emotions is known as "loving kindness" or "compassion" practice. In this practice, mental talk and/or image is used to evoke positive feelings which are then directed towards one's self and towards others. Many objective triggers of positive emotions can also be used: music, photos of loved ones, gazing at beautiful scenery, etc. Because we generally get good at what we practice, including mental states, over time such practices can reinforce the neural circuits associated with the positive emotions making them more readily available in life. One downside of working with positive emotions in this way is that the practice can become something of a "safe harbor" where we escape from more challenging emotions. So it is a good practice to balance these practices with some of the more challenging work to make sure we are processing our stored-up reactive emotional scar tissue.
The process of evoking or triggering challenging emotions works the same way, but in reverse. For evoking, we call up thoughts that we anticipate will cause a MANAGEABLE level of challenging emotions to arise. Triggering might use photos or voice recordings to do the same thing. Triggering also may use challenging physical ordeals such as long sitting, breath restriction, or some shamanic or ascetic practices like the Sweat Lodge. Now you might wonder why when I just got through saying we get good at what we practice we would want to practice uncomfortable or unwelcome emotions. The answer is that when we process challenging emotions with concentration, clarity, and equanimity (C,C, and E), instead of reinforcing those neural patterns, we actually deactivate the stored-up emotionally reactive scar tissue mentioned above. The key to getting the benefits from evoking or triggering challenging emotions is to try to keep the emotional activation limited to an intensity at which you can maintain some level of C, C and E. If you are stirring up emotions that are too intense, you will not be able to get much benefit from the practice. This is one of the problems faced by people with PTSD: as soon as they open the door to the arising of challenging emotions, they get blown away by the intensity. But for most people, these evoking and triggering practices can be very fruitful.