First thing to note is that the DC to AC conversion is not directly linked to the functionality of the solar cell. Power from a solar cell can be used without a conversion to AC.  However since the power grid runs on AC for most stationary use cases it makes most sense to convert it to AC.
But back to the conversion question. As the name suggest, in AC current the current and voltage are oscillating. This means they change their direction frequently. For Europe this is most commonly 50Hz. Moreover when talking about AC nothing is said about the shape of the current. For the power grid its a sine wave, however for laboratory uses other versions like rectangle or triangle are also possible. 
DC current on the other hand keeps its polarity constant. To convert DC to AC the DC current is pulsed, meaning it gets turned on and off in a fraction of a period of the AC current. In this way the AC sine wave is simulated, however it stays an approximation. It starts with very short pulses. At the pike of the sine wave it gets the longest pulse and than they get reduced again. When the sine wave changes its direction the polarity of the DC source is switched and the pulsing starts again.
For the use case of putting power into the grid it is also important that the girds sine wave is followed, meaning there should not be a phase offset between the grid and the from the AC conversion generated current.
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