"What a first week!" This is an exclamation. Simply stated, it indicates that the initial week (possibly at school or work), had elements of surprise, frustration or busyness that left the person feeling perhaps a little overwhelmed. The activities that occurred during the week could have been challenging or fruitful or amazing, or exhausting. The exclamation does not indicate whether these occurrences were good or bad, but just that they were probably unexpected. Thus, this phrase may express either horror or adulation, depending on what happened during the week. This is a rather complicated answer to your question. I hope it doesn't confuse you even more. Unfortunately there is a lot of pragmatic detail that relies on context to completely understand this comment.

This is an emphasize phrase .In your example it is used to express how the first week of school or job or whatever was full of ups and downs and surprises and all kinds of craziness or happiness that made it unusual or special. "What a ..." can be used before anything! What a concert! That band is so great! What a pretty girl ! What a beautiful day it is? What a wonderful trip I had !

Usually, when someone says this they mean that the first week (at a job, at school, in a new place) was eventful. This could be either negative or positive, it depends on the context. After my first week at a new job, I might tell my friend "what a first week!" to let her know that a lot of things (good or bad) happened at work.