Author's note: I myself am an INTJ, therefore Si is not in my main function stack. I have compiled the best information I can from what I found from Career Planner, The Career Project and Quora answers, however, I cannot provide any personal anectodes.
Introverted Sensing is an introverted and perceiving function. Si users use information from the past to inform the present, allowing them to compare and contrast what is currently happening to what has happened before.
I found this here: Dominant and auxiliary Si users tend to learn from experience and continue to build incrementally. They tend to be risk-averse and less open to novelty or change. They tend to have good concrete memories (like for dates, credit card numbers, the clothes someone was wearing at an event, etc.) and attention to concrete details.
I also found this here: Si focuses on the subjective, internal world of personal experience and compares and contrasts new experiences to past experiences and memories. Si users tend to notice patterns repeating themselves and are quick to spot changes or inconsistencies in their environment. They trust personal experience and subjectively explore the impact of current events, choices, and consequences.
Si users are also more in tune with their internal sensations (e.g. pain, hunger and thirst), whereas Se users are more in tune with external sensations (what they can perceive with their 5 senses).