C++ STL allocator vs operator new
The two are not contradictory. Allocators are a PolicyPattern or StrategyPattern used by the STL libraries' container adapters to allocate chunks of memory for use with objects.
These allocators frequently optimize memory allocation by allowing * ranges of elements to be allocated at once, and then initialized using a placement new * items to be selected from secondary, specialized heaps depending on blocksize
One way or another, the end result will (almost always) be that the objects are allocated with new (placement or default)
Another vivid example would be how e.g. boost library implements smartpointers. Because smartpointers are very small (with little overhead) the allocation overhead might become a burden. It would make sense for the implementation to define a specialized allocator to do the allocations, so one may have efficient std::set<> of smartpointers, std::map<..., smartpointer> etc.
(Now I'm almost sure that boost actually optimizes storage for most smartpointers by avoiding any virtuals, therefore the vft, making the class a POD structure, with only the raw pointer as storage; some of the example will not apply. But then again, extrapolate to other kinds of smartpointer (refcounting smartpointers, pointers to member functions, pointers to member functions with instance reference etc. etc.))
For general programming, yes you should use new and delete.
However, if you are writing a library, you should not! I don't have your textbook, but I imagine it is discussing allocators in the context of writing library code.
Users of a library may want control over exactly what gets allocated from where. If all of the library's allocations went through new and delete, the user would have no way to have that fine-grained level of control.
All STL containers take an optional allocator template argument. The container will then use that allocator for its internal memory needs. By default, if you omit the allocator, it will use std::allocator which uses new and delete (specifically, ::operator new(size_t) and ::operator delete(void*)).
This way, the user of that container can control where memory gets allocated from if they desire.
Example of implementing a custom allocator for use with STL, and explanation: Improving Performance with Custom Pool Allocators for STL
Side Note: The STL approach to allocators is non-optimal in several ways. I recommend reading Towards a Better Allocator Model for a discussion of some of those issues.
Edit in 2019: The situation in C++ has improved since this answer was written. Stateful allocators are supported in C++11, and that support was improved in C++17. Some of the people involved in the "Towards a Better Allocator Model" were involved in those changes (eg: N2387), so that's nice (: