Suicide is an unofficial term used to describe when a monster purposely attacks another with an equal or greater ATK, which (on success) would guarantee the said monster to be destroyed (sent to graveyard). This is in opposite with the standard approach of not attacking monster that would cause the attacker monster to be destroyed in the process. This is also commonly called ramming, kamikaze, or - in cases when the monsters have equal ATK - a double KO or crashing. It is worth noting that if two monsters with 0 ATK attack each other, neither will be destroyed.
This can be used tactically to activate effects that only work when a monster is sent to the Graveyard by battle, such as those of "Pyramid Turtle", "XX-Saber Emmersblade", "Exploder Dragon", "Dark Necrofear", "Gigantes" or "D.D. Warrior Lady". The loss to your Life Points is often worth the field advantage you gain through those effects (loss of LP does not apply to an attacking "Exploder Dragon", however). This tactic is often more useful than waiting for your opponent to destroy said monsters by battle, as the opponent may suspect these monsters and try to destroy them with card effects instead.