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I've heard that unlike Tokamaks that use magnetic confinement of the plasma, the NIF project uses 'inertial' confinement. What's inertial about it? Do they spin the plasma to use angular momentum like in a gyroscope?

From a naive perspective it looks like the pressure of the lasers are what's confining the plasma.

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    $\begingroup$ It's called inertial confinement because a hot exploding shell of material is used to create shock waves around a cold core. The heating pulse is ideally shorter than the implosion and as the shockwave travels inward it compresses and heats the core material. The peak density can only be sustained for a very short amount of time before the internal pressure generated by the heating by the shockwave and the fusion reaction overcome the inertia of the material and the pressure and temperature fall below the fusion threshold, again. $\endgroup$ – CuriousOne Oct 8 '14 at 0:13
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    $\begingroup$ I'm no plasma physicist, but I believe that the naming is due to a similar idea with nuclear weapon tampers. The high mass of the enclosure enables the plasma inside to reach a very high pressure simply because it "won't easely move out of the way" while the plasma in the beggining stages. Edit: CuriousOne answered just before I did, please disconsider my comment $\endgroup$ – Hydro Guy Oct 8 '14 at 0:14
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The comments basically answer the question. Another answer is found on HyperPhysics by Rod Nave:

While magnetic confinement seeks to extend the time that ions spend close to each other in order to facilitate fusion, the inertial confinement strategy seeks to fuse nuclei so fast that they don't have time to move apart.

Directed onto a tiny deuterium-tritium pellet, the enormous energy influx evaporates the outer layer of the pellet, producing energetic collisions which drive part of the pellet inward. The inner core is increased a thousandfold in density and its temperature is driven upward to the ignition point for fusion. Accomplishing this in a time interval of $10^{-11}$ to $10^{-9}$ seconds does not allow the ions to move appreciably because of their own inertia; hence the name inertial confinement.

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