MEATER Block does not have an internal battery, so plugging it in won't charge it. This also won't recharge your AA batteries, even if the batteries are rechargeable. Always make sure to recharge your AA batteries in their own charger.
Plugging in your MEATER Block is useful if you want to save your AA batteries, especially during long cooks. When the charger is plugged in, this takes precedence over the AA batteries to power MEATER Block.