What are uses of the C++ construct "placement new"?

It allows you to do your own memory management. Usually this will get you at best marginally improved performance, but sometimes it's a big win. For example, if your program is using a large number of standard-sized objects, you might well want to make a pool with one large memory allocation.

This sort of thing was also done in C, but since there are no constructors in C it didn't require any language support.

It is also used for embedded programming, where IO devices are often mapped to specific memory addresses

Its usefull when building your own container like objects.

For example if you were to create a vector. If you reserve space for a large number of objects you want to allocate the memory with some method that does not invoke the constructor of the object (like new char[sizeof(object) * reserveSize]). Then when people start adding objects into the vector you use placement new to copy them into allocated memory.

template<typename T>
class SillyVectorExample
{
    public:
        SillyVectorExample()
            :reserved(10)
            ,size(0)
            ,data(new char[sizeof(T) * reserved])
        {}
        void push_back(T const& object)
        {
            if (size >= reserved)
            {
                // Do Somthing.
            }
            // Place a copy of the object into the data store.
            new (data+(sizeof(T)*size))  T(object);
            ++size;
        }
        // Add other methods to make sure data is copied and dealllocated correctly.
    private:
        size_t   reserved;
        size_t   size;
        char*    data;
 };

PS. I am not advocating doing this. This is just a simplified example of how containers can work.

I've used it when constructing objects in a shared memory segment.