Cimarron explained the basics quite well. Si is basically about retaining facts and data. When you're remembering anything, you're using Introverted Sensing. All information that you remember is taken in with your five senses, and then you use Introverted Sensing to maintain and recall it. Introverted Sensing is also, like Cimarron said, about taking in information via your five senses and then comparing it to what you already know.
Every person who has Introverted Sensing is an SJ. There are Extraverted SJs and Introverted SJs, though. An Extraverted SJ, or an ESxJ, uses Introverted Sensing to perceive and maintain the data they take in while interacting with the world with their extraverted judging function, thinking or feeling. So, an ESxJ uses Introverted Sensing to serve their Extraverted judging function, and to maintain order in the external world as a main priority.
An ISxJ, though, since they're Introverted, are more focused internally on their own subjective opinions and thoughts. Their dominant function is Introverted Sensing, which they will be the most experienced using. Unlike an ESxJ, they use their secondary Extraverted judging function to serve the needs of Introverted Sensing. Introverted Sensing is concerned with the facts of concrete reality. An ISxJ will want a wealth of information before interacting with the external world with their Extraverted judging function.
ISTJs are more focused on the impersonal end of interaction with the external world, and will seek objective information. ISFJs, however, are more focused toward using their Introverted Sensing to maintain concrete facts about the people around them.
Extraverted Sensing is about adjusting yourself to adapt to the external world. Introverted Sensing, however, is more deliberate. Since Introverted Sensing focuses on holding a vast amount of facts and data about the world, a person who uses Introverted Sensing will adjust the outside world to adapt to the experiences of the person. Introverted Sensing relies greatly on experience, what is happening now and what happened in the past. The person with Introverted Sensing looks to their own experiences to deal with immediate sensory concerns. If they don't have experience to match the situation, they have great difficulty facing it. Like I said earlier, all users of Introverted Sensing are of the SJ temperament. They will interact with the external world with judgment rather than perception.
Even, from my own experiences, which Jack Flak has brought up that you're not supposed to do that much, I've seen Introverted Sensing in action a lot. For instance, I was talking to a career counselor that is also MBTI certified. I spent 20 minutes talking to her about my college plans and then she brought up MBTI stuff to compare to my career choices. I outright told her, "I don't care about MBTI and I'm not applying it to my own personal choices. I'm relying on my own experiences of what I've done well and what I enjoyed, and going from there." I instantly realized right then that that was a very SJ thing to say. I didn't want to take external facts into consideration for my own decisions. It's the same with just about every decision I make. I have a very difficult time doing things as they come up. I need to take time to understand what it is I have to do and why I'm doing it regardless of how big or small of a thing it is. It just makes me wildly uncomfortable.