So, when we talk about words and sentences, some of them can be really easy to understand without even knowing what they mean! Like, if I say "the sky is blue", you might not know what "sky" or "blue" mean, but you understand that the sentence means "the thing up there that isn't a building or a tree is a certain color". This is because the sentence is "analytic". It's made up of words that we already know, and the meaning is just a combination of these words.
On the other hand, there are sentences that don't make sense unless you know what some of the words mean. Like, if I say "timonousj donkablab meep", that doesn't really mean anything to you because those words aren't in your vocabulary. So you might say that this sentence is "synthetic", because its meaning comes from the combination of the words rather than just each individual word by itself.
So, the "analytic-synthetic distinction" is just a way of talking about the difference between sentences that you can understand just by knowing what the words mean, and sentences that only make sense if you know what some of the words mean. It's kind of like the difference between a puzzle where you already know what all the pieces look like, and one where you have to figure out what the picture is by putting the pieces together in a certain way!