A physical core is what it sounds like - an actual physical processor core in your CPU. Each physical core has its own circuitry and its own L1 (and usually L2) cache can read and execute instructions separately (for the most part) from the other physical cores on the chip.
A logical core is more of a programming abstraction than an actual physical entity. A simple definition of a logical core is that it is a processing unit that is capable of executing its own thread in parallel with other logical cores. In fact you could say that a logical core is the same as a thread.
You can have multiple logical cores per physical core. However logical cores share resources with other logical cores operating on the same physical core, so having more logical cores will not necessarily get you the same performance increase as having more physical cores.
In the case of intel hyperthreading (HT), you have two logical cores per physical core, so a quad-(physical) core i7 processor will have eight logical cores. However the two logical cores within one physical core cannot truly operate in parallel with respect to each other. This is because HT works by having one logical core operate while the other logical core is waiting and has nothing to do (for example when it is waiting on a cache or memory fetch).
Well then how can these logical cores be considered in parallel? Well most of the time they can be because during typical CPU operation you will almost never see continuous execution of a single thread on every clock cycle - there are always gaps when one logical core is waiting for something and the second logical core can kick in and do its job.
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