It's the usual problem: affected batteries may overheat or even ignite, potentially burning the user or starting a fire.
The batteries covered by the recall are used with the following Portege, Satellite, Satellite Pro and Tecra models sold between June 2011 and September 2015:
C50, C50-A, C50D-A, C640, C650, C650D, C660, C660D, C70, C850, C850D, C870
L630, L640, L650, L650D, L670, L70, L70-A, L730, L740, L750, L750D, L770, L830, L840, L850, L850D, L870
P70-A, P750, P770, P840, P850, P870
R700, R830, R840
Toshiba's website provides instructions for locating the part number and requesting a replacement.
The affected items have battery part numbers starting with G71C and various accessory part numbers starting with PA3 or PA5. Toshiba's Battery Check Utility (available via the above link) reveals whether the installed battery is covered by the recall, avoiding the need to remove and inspect the battery.
It's the usual story - if your battery has been recalled, stop using it immediately. You can continue to operate the computer on mains power even if a battery is not fitted.