Philosophical analysis means trying to understand things by breaking them down into smaller pieces and examining each of those pieces carefully.
Let's say you have a toy car that you really like. You could do a philosophical analysis of it by asking different questions about it.
For example, you could ask what the car is made of - is it plastic or metal? You could ask how it moves - does it have wheels or does it slide? You could ask why you like it so much - maybe it's the color, or the fact that it reminds you of a real car you saw somewhere.
By asking all these questions, you might start to understand the toy car better. You might also start to see connections between different parts of the car - for example, maybe the color is important because it matches the real car that you saw, or maybe the fact that it slides instead of having wheels makes it easier to play with on your carpet.
Philosophical analysis can be applied to all sorts of things, from toys to ideas to scientific theories. It's a way of trying to understand things by breaking them down and looking at them carefully, piece by piece.