Have you come across the word se (self, oneself)? Well, si is basically a dative form of it (to/for oneself).
In this case, using si makes a slight difference in meaning, it makes it reflexive ('referring back to the subject of the sentence'). Let me demonstrate:
Ten den pamatuju. = 'I remember that day.', 'I recall that day.', 'I keep that day in mind.', 'I witnessed that day.'
Ten den si pamatuju. = 'I remember that day (for) myself.' 'I recall that day (for) myself.' I keep that day in my mind.'
You may wish to consult the tips & notes sections as well.