Just to elaborate on the above answer. Impedance is the measurement of electrical resistance measured in ohms. Your sub-woofer has a stated resistance typically 4 or 8ohms. Amplifiers are designed to operate safely and stable so long as the load (a.k.a speaker) resistance is the same or greater than this specification. If you are connecting only one speaker then you have nothing to worry about as most modern amplifiers (car audio specific) are stable down to around 2ohms, several go as low as .5ohms.
The 800watts is the maximum power the speaker is designed to accept without failing either electrically or mechanically.
Your amplifiers 300watt rating is (if accurately published) the maximum it is capable of producing. So from strictly a power standpoint your amp shouldn't be capable of producing enough power to damage that speaker.
Keep in mind however manufacturers are notorious (car audio specifically) of over rating their equipment. A shady manufacture may state their speaker is 800watts, but that measurement is peek and not RMS. Meaning that the speaker can take 800watts for a split second but not continuous (RMS).
In any case just from these numbers, if accurate, your amp should drive that speaker with no problem and you should not have much worry about causing damage if the box the speaker resides in is appropriately matched.