Impulse drive
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In Star Trek, the impulse drive is the sub-light speed engine that the starships use when they are not travelling at warp speed or in hyperspace. It allows ships to travel non-stellar distances fairly quickly. For example, Starfleet Academy cadets use it to practice flying to Saturn and back.
There are practical challenges surrounding implementation of this technology. Generally there are three major problems: acceleration, time dilation and energy. The acceleration aspect is usually explained as being dealt with through the use of inertial compensators. Time dilation would become noticeable at appreciable fractions of the speed of light. The energy use aspect is more difficult to explain without examining how the system functions.
In the television series and books, there have been two descriptions of how it works. The most common description is that it is analogous to a rocket and performs as a reaction-based thruster. The less common (but more plausible based on the exhibited performance) is that it uses gravitational distortion to create a 'wave' through space that the ship essentially 'surfs'. This would be consistent with the concept of "one half impulse" and "full impulse" being measures of absolute speed instead of acceleration, as a reaction drive would indicate. Of note, the latter description is similar to some descriptions of the warp drive, as a character in the book Enterprise notes, but another character waves that away as being an 'oversimplification'. As this technology pertains to a fictional show, there is endless room for argument without any definite means of resolution.