Solo masturbation is the sexual stimulation of one's own genitals for sexual arousal, normally with the goal of reaching an orgasm. This stimulation may involve fingers, hands, sex toys or in times of dire need, household objects. Reading sex stories or having sexual fantasies often speeds up the process!
Mutual masturbation is masturbation with a sexual partner, and usually includes manual stimulation of a partner's genitals with fingers or instrumentally with the use of objects.
Masturbation is colloquially referred to as "self-abuse", "playing with yourself", "fingering", "touching yourself", "bringing yourself off", "jerking off", "frigging", "wanking" and "pleasuring yourself". Other humourous euphemisms include "polishing the pump", "auditioning the finger puppets", "paddling the pink canoe", "Jillin' off", "Lone Rangering" and "giving yourself a hand", amongst others.