Plasma Charges are the upgraded form of C4 Explosive Charges, and as such are primarily intended for destroying terrain rather than enemies. However, the advanced alien materials involved give it a much stronger bang than its earthly predecessor.
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To use a Plasma Charge, you must first put it into the soldier's Primary Weapon slot. Left-click on it there, and a small number pad will appear; use this to set the charge's timer at a cost of 2 TU's, or right-click to disarm the timer. You then get a throw cursor; it costs 60% TU's to throw, or you can of course right-click to dismiss the cursor. Left-clicking on an armed Plasma Charge will let you reset the timer.
Be warned; the Plasma Charge will explode once its timer runs out - regardless of whether the soldier is still carrying it.