The d20 System has several design strengths over earlier gaming systems, which make the game easier to play. They are:

Roll high
Whenever a player is rolling a die to do anything, they always want to roll high. There are no good effects to be gained by rolling low. Ever.
Higher is better
For any ability or statistic that a player has, they always want a high number. Gone are the days of trying to minimize your THAC0 and AC while increasing your hit points.
Positive is good
Notice a trend yet? Anything which modifies a number is good if it is positive, and bad if it is negative.
Use of formulas
Instead of using lookup tables for finding values, almost any value is derivable from a simple (usually linear) formula (the one exception to this seems to be max carry weight).
Precomputability of modifiers
Most modifiers can be easily precomputed, such that a player rolls a die, adds their combined modifier, and checks to see if the roll was high enough to be successful.