Super Saiyan is a transformation achieved by pure-hearted Saiyans (Whether good or evil) that experience pure emotional rage or some other extremely motivating cause (like being nearly killed). This transformation powers the user up to fifty times more then the base state Saiyan's power. Goku is the first to achieve this form, after witnessing Frieza killing his best friend, Krillin. Future Trunks also achieves this form, with his father Vegeta following suit. Later, Goku's two sons Gohan and Goten achieve this form, along with the present-timeline Kid Trunks. The alternate timeline versions of Gohan, Vegeta and Goku also were shown to achieve this form.
Many fans are confused of how Goten and Trunks managed to become Super Saiyans as they never experienced any large emotional rage, Goten's transformation can be explained as before he was concieved Goku was already a super saiyan. Trunks' transformation however, cannot be explained