For example, here's your basic Imperial Guardsmen, common human soldier.
BS 4+
Toughness: 3
Sv: 5+
With a humble Lasgun, Strength: 3, Damage: 1, AP: 0
If he shoots himself in the foot, he needs to get a 4, 5 or 6 on a six sided dice to hit so 50%, then you compare Strength to Toughness, since those values are equal you need a 4+ to wound (consult the table below), so another 50% chance for a 25% chance to wound before armor/ward saves. Since you have 5+ armor, that's a 33% chance to negate damage with no AP on the attack on a roll of 5 or 6, so that 25% chance drops down to a 16.5% chance to wound and deal damage. If this weapon had AP -1, you reduce the armor save roll by 1 point, so only a dice roll of 6 reduced by 1 point to a dice roll of 5 can stop the attack, giving you a 21% chance to deal damage instead.
A ward save is the exact same thing as armor/except it's not reduced by AP on weapons, so it usually represents things like magic or psychic abilities or technological force fields.