In Japanese grammar, what is the difference between wa (は) and ga (が) particles?
user
Japanese particles は (ha/wa) and が (ga) are often picked out as the most confusing area of Japanese study, and it continues to be confusing right the way through from beginner to advanced level. 
From a grammatical point of view, が goes after a word or phrase to pick it out as the subject of a sentence, or part of a sentence (a "clause"). That is, the person or thing before が is doing or being something. It's the protagonist. Grammatically, it's a relatively defined and straightforward role. An example might be:
子供が 遊んでいる。(A child is playing.)
子供 (child) comes before が here, showing us that 子供 is the subject. In other words, 子供 is the person doing the action of "playing." 子供 is the "perpetrator," and we know this because が is helpfully making this clear.
は, on the other hand, isn't picking out a specific part of a sentence and telling us its exact grammatical role within that sentence. Rather than showing us our subject, or object, or some other grammatical building block, は is doing something quite magical that most languages can't do explicitly in this way: it's telling us the topic of our sentence, or part of a sentence, or maybe a whole paragraph or more. Here's an example:
東京は 賑やかな 所です。(Tokyo's a lively place. / As for Tokyo, it's a lovely place.)
Both wa (は) and ga (が) show us where emphasis lies, and in doing so they make a distinction between information that is already in our consciousness and information that the speaker or writer wants to introduce — or re-introduce — into our consciousness.
assistant
I still don't quite get it - you're making it seem like both particles are interchangeable, but at the same time not. So, just to make things clearer on a concrete example: please explain the difference between 子供が 遊んでいる and 子供は 遊んでいる. I am not a native, or anything even close, so if 遊んでいる is not in the right clause, please ignore it and concentrate on the が vs は part.
user