A tablet can mean a small, flat computer with a touchscreen, or a small solid piece of medicine that you swallow. Historically, it also meant a flat slab used for writing.
It comes from Old French 'tablete', a diminutive of 'table', from Latin 'tabula' meaning 'board or writing surface'. The idea of 'small flat surface' carried over into medicine and modern electronics.
Your digital tablet is named after ancient clay tablets people scratched writing into thousands of years ago. The shape—small, flat, and portable—stayed the same, but the 'writing' turned from carved marks into glowing pixels.
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