The difference is desperately complicated as Ranier mentioned. Basically, WA emphasizes the sentence object, and on the other hand, GA has the readers focused on its sentence subject. Watashi HA Kevintehabla desu. (Who’re you? / I am Kevintehabla.) Watashi GA Kevintehabla desu. (Who’s Kevintehabla? / It’s me.) Watashi HA ring wo tabemashita. (Did you eat the apple? / I ate that.) Watashi GA ring wo tabemashita. (Who ate the apple / I ate that.)

in a simple sense, wa is talking about the subject while ga isn't necessarily. わたしは社長です。 i am the boss. (talking about ME. you would say this when describing yourself) わたしが社長です。 i'm the boss. (talking about who the boss is. the boss happens to be me. you wouldn't say this when talking about yourself, only when saying who the boss is.) that is the most basic difference but there are many, many more. if you looked in a proper grammar book there is probably 200 pages on this topic so they couldn't all be covered here....