The BIOS battery (aka CMOS battery) is totally separate to the main laptop battery. The BIOS battery is what keeps a computer 'powered up', so that memory settings aren't lost, when it's switched off. The first sign of a BIOS battery starting to fail is usually when the computer's time and date settings keep going awry.
Replacing a laptop battery usually takes just a a few seconds. (Just release a couple of catches, slide the old battery out and slide the new one in). Replacing a BIOS battery (which is usually a 'coin' battery can be a lot trickier, depending upon
(a) how easy it is to get inside the machine ; and
(b) how the battery is connected up. (Some BIOS batteries are simply slotted into holders, and can be removed by just pulling them out, but others are actually soldered to the leads that they connect to).
I've never seen an on-screen message about a failing BIOS battery but I suppose (based upon you seeing a reference to 'BIOS' in the message that briefly appeared) that it might be the case here. Keep an eye on the date and time that your laptop is displaying!