Hyper-threading is using one processor but logically dividing it into two so that it gives the user the benefit of two processors with only using the resources equivalent to almost one. This is achieved by sharing, partitioning and duplicating the various resources almost into two processors. Used by the latest Pentium processors, which are HT enabled, in layman's terms, it allows you to use more than two applications at the same time without slowing down processing speed.

Multi-threading is when various processes are time sliced such that it gives the user the impression that all the programs are being run at the same time. This is what happens on your computer regularly.

Super-threading allows threads from different processes to be executed at the same time unlike Multi-threading where every process has a time slot during which, thread from only one process will be executed. But every time, if for example, there are four instructions issued to the processor. They will all be from the same process. Hyper-threading takes it a step further. It allows threads from different processes to be issued at the same time, in turn, utilizing the waste cycles of the processor. You can go to any Intel site for further info on this.

Another answer:

Super-threading is a multithreading approach that weaves together the execution of different threads on a single processor without truly executing them at the same time. This qualifies it as time-sliced or temporal multithreading rather than simultaneous multithreading. It is motivated by the observation that the processor is occasionally left idle while executing an instruction from one thread. Super-threading seeks to make use of unused processor cycles by applying them to the execution of an instruction from another thread.

Multithreading computers have hardware support to efficiently execute multiple threads. These are distinguished from multiprocessing systems (such as multi-core systems) in that the threads have to share the resources of single core: the computing units, the CPU caches and the translation lookaside buffer (TLB). Where multiprocessing systems include multiple complete processing units, multithreading aims to increase utilization of a single core by leveraging thread-level as well as instruction-level parallelism. As the two techniques are complementary, they are sometimes combined in systems with multiple multithreading CPUs and in CPUs with multiple multithreading cores.

Hyper-threading is Intel's trademarked term for its simultaneous multithreading implementation in their Pentium 4, Atom, Core i7, and certain Xeon CPUs. Hyper-threading (officially termed Hyper-Threading Technology or HTT) is an Intel-proprietary technology used to improve parallelization of computations (doing multiple tasks at once) performed on PC microprocessors. A processor with hyper-threading enabled is treated by the operating system as two processors instead of one. This means that only one processor is physically present but the operating system sees two virtual processors, and shares the workload between them. Hyper-threading requires both operating system and CPU support for efficient usage; conventional multiprocessor support is not enough, and may actually decrease performance if the Operating System is not sufficiently aware of the distinction between a physical core and a HTT-enabled core. For example, Intel does not recommend that hyper-threading be enabled under Windows 2000, even though the operating system supports multiple CPUs (but is not HTT-aware).

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