The report Lamborghini submitted to NHTSA says the issue lies with the gas tank's EVAP system. Liquid fuel can get into the EVAP system if an owner overfills it or in "particular handling situations," which we assume includes hard acceleration and cornering that sloshes the fuel around. If the fuel gets into the EVAP system, flammable vapors can escape. These vapors could potentially ignite, and the report states that high revving at a stop or using an aftermarket exhaust increases the danger due to the possibility of flames coming from the exhaust.
According to NHTSA documentation, owners of affected vehicles will be notified of the issue by Lamborghini, and they will be able to schedule a time at the dealer to have the EVAP system fixed. The remedy includes a new type of purge valve, and the change will be done for free. Also, owners of the new Aventador S and the latest versions of the Aventador SV have nothing to worry about, since their cars already have the new parts. As for other Aventador and Veneno owners, we'd recommend not filling up your cars quite so full, and maybe don't show off at stop lights too much until the car is fixed.