"This is the woman."
I am Jewish, Hebrew is my second language, so I know what I am saying. We wrote the same thing except for זאת which he pronounced like a Sephardi (someone originally from Spain) and I pronounced like an Ashkenazi (someone from Germany or almost anywhere else in Europe). זו is sometimes zoe (like toe) and sometimes zo (like two).
All of them mean "this". However, their position and function is different. זה and זאת are demonstrative pronouns and are followed by nouns:
This is a man - זה גבר
This is a woman - זאת אישה
On the other hand, הזה and הזאת are determiners and they follow the noun, which is always definite:
I love this man - אני אוהב את הגבר הזה
I help this woman - אני עוזר לאישה הזאת.