Strength measures how strong you are, how well you can take a punch, and how well you fight unarmed.  People with high Strength aren't hurt easily, especially by blunt attacks.  (Think of it somewhat like armor.)  It also measures your athletic ability, how coordinated you are, and your overall ability to do physical stuff without tools (climbing, acrobatics, jumping, swimming, etc).  A person with high enough strength can punch through armor and does greatly enhanced damage with weapons if he hits [though the hitting itself is determined by warfare].

High Strength helps you to:

Levels of Strength

Human (-25)

You have the strength of an average human, which means that in the Amber scheme of things, you're feeble.  The average Amberite can crush you like a bug in hand to hand combat, and anyone above Amber rank will run wild over you without even noticing.

Chaos (-10)

You're ready to do pro wrestling or professional weight lifting or professional martial arts.  This is the average rank in Chaos, while in Amber someone at this rank is considered somewhat weak.  Anyone with 1 or more points can still beat you down, but it may take a little time if they don't have too many points.

Amber (0)

You're ready to trade tips with Bruce Lee.  You are a skilled unarmed combatant, easily beating those of Human rank and defeating those of Chaos rank with effort.  Only those with 76 or more points of Strength can one-punch you if you're ready for them.

Bottom Ranked (1-10)

Amberites who do a lot of fighting or hard physical labor will generally be found in this range of points.

Low Ranked (11-20)

People at this level are considered strong in Amber.

Middle Ranked (21-50)

This is the realm of the consumate professional, that of those who train others in unarmed combat.

High Ranked (51-75)

This is a very exceptional level of strength, possessed generally by only the best.  You're strong enough to break through 1 point armor with your fists.

Best Ranked (76-125)

You knock down trees, kill warhorses with a blow to the head, and juggle members of the Royal Family for fun.  They can't stop you, after all.  You can pull stunts like watching someone eat breakfast and tell how good they are at unarmed combat and what style they practice.  You can break through 2 point armor with your fists, and given enough time, shatter things with 4 point armor.  You can one-punch just about anyone with Amber strength or less, unless they have goatloads of Endurance.

Exalted (126+)

You beat down Gerard every morning before breakfast and in the afternoon before dinner.  Then you walk into shadow and crush Hercules and Atlas at the same time before you go to bed, in order to help you sleep.  You can punch through 4 point armor, and given enough time, you can break through 8 point armor.  You can one-punch anyone with 10 or less points of Strength, unless they have goatloads of Endurance.