These kinds of meditations cultivate our ability to witness our thoughts and emotions without getting attached to them, identifying with them, or judging them.
Mindfulness meditations are in this category, as are Vipassana, satsang, self-inquiry, Vedanta, non-dualism, jnana yoga, Zen, and a variety of Buddhist practices.
In addition to cultivating the capacity to witness our thoughts and emotions, without attaching to or judging them, another feature of insight meditations is that they will often call into question the ego identifications that we have created and believe ourself to be.
In Jnana yoga the primary practice is to constantly watch how our thoughts are often preceded by the 'I am' statement. We constantly are telling ourselves things like, 'I'm hungry, I'm sad, I'm a father, I'm an accountant, I'm confident, I'm right....ad infinitum, we tell ourselves we are something. If we examine this closely we can find that there is usually some kind of identification behind the 'I am' statement. Therefore, whenever we have a thought that is preceded by the 'I am' statement, we can bet that some identification is sure to follow. When we say 'I am hungry,' we are identified with our bodies physical needs for food. When we tell ourselves something like 'I'm upset,' we are identified with frustration, worry, anger or any number of other feelings and emotions that are making us upset. We identify with our work and profession when we say things like, 'I'm a teacher at this school.'
Through the 'I am' statements we use we are re-enforcing our identifications of who we believe our self to be. This can be a positive thing as when we tell ourselves empowering beliefs about our identity, but this can also be a disempowering thing when we identify with negative emotions, thoughts or self-limiting beliefs. When we are identified with our negative emotions, negative beliefs, limitations and negative self talk, we will suffer. In some of the Eastern traditions it is believed that much, if not most of our psychological suffering, comes from our identifications with our negative thoughts and emotions. Therefore, one of the practices and tools that we will use to become more mindful is to watch how we use the 'I am' statement in our interior realties and thoughts.
When we experience ourselves in thought, as an 'I am' statement, we are literally identified with whatever follows the 'I am' statement. Therefore, if we say 'I'm not good enough for this,' we are creating, and identifying with, a self-limiting belief about who we think we are. By developing the ability to watch our thoughts, or to witness and observe them, without getting identified with them, we will have acquired a very useful skill that can bring greater mindfulness, inner peace and awareness to our lives.
Watching the 'I am' statements can also be useful to help us form positive identities and thoughts. When we feel good, it is equally important to notice the 'I am' statements that we are using and identified with. When one says something like 'I'm a mother,' there may be a great joy, love or feeling of achievement that comes from that. When we learn to identify the positive 'I am' statements we use in our lives, we can often build on the very things that make us feel good.
In summary, insight meditations teach us to watch our thoughts in a mindful, nonjudgemental way, that creates some space between our thoughts and our identification with them. By learning to witness and observe our thoughts, rather than be completely identified with them, we can produce a multitude of positive changes.