Strength is a skill in which when developed it increases your maximum damage towards the one your facing. Strength is one of the key ingredients of creatinga worthy stand to your opponent as when you develope your combat you'll require higher standards of damage. Attack doesn't actually necessarily help strength but has a strength bonus which indeed does boost your damage. Attack is mainly a skill to help increase the melee accuracy "how often you hit damage".

A true player in combat will require all the skills and have a good mix instead of the ones focusing on strength based Rnge 2h. Strength doesn't increase the chance of hitting armour that is stronger then your weapon as that is attacks job. Currently strength is the most common skillcape in all of RuneScape.