Si is about connections in readily observable processes.
Being a dynamic information element, Si sees activity. It's about something happening, or "processes". See examples below.
For Si, "readily observable" sometimes means that it's immediately apparent to the person experiencing whatever it is that's going on (though it can also mean "readily observable" as in the example below). If someone is experiencing discomfort because of back pain, that person may be the only one who knows it, but it's still immediately apparent to that individual. In this example, the "connections" are between the person, the pain, and the resulting experience of discomfort.
A person can see those "connections" between other things/people too though. A good example may be the workings of a machine. In this example, it may be easiest to compare and contrast Te and Si. As the gears are turning and the motor is running and whatnot, Te sees the activity of each of these components in and of itself. Si, on the other hand, sees the connections between each of those components, how one gear turns another which is causing something else to happen.
Edited to add: The ability to see these "connections in readily observable processes" is what compels/allows Si types to be good at taking care of people and being attentive to their needs.