From NCLR (pdf):
Judge Walker struck down Prop 8 on Wednesday, August 4. On the same day, Judge Walker also temporarily “stayed” his decision, which means that the ruling isn’t effective right away. The Judge will decide whether to “stay” the decision for longer after all the parties respond to the Yes on 8 request for a longer stay. All responses have to be filed today, Friday, August 6.
Both California Attorney General Brown and California Governor Arnold Schwarzenegger filed responses opposing a stay and urging the court to let its decision take effect immediately so that same-sex couples in California can begin to marry. The plaintiff couples also are strongly opposing a stay.
Judge Walker can decide whether to stay the decision for longer at any time. If he grants the motion to stay, same-sex couples will not be able to marry in California until after the appeal is finished. The Judge can also delay the decision for a short time until the Ninth Circuit appeals court decides whether they will order a stay.
If Judge Walker denies the stay and permits his decision to take immediate effect, the Yes on 8 proponents can ask the Ninth Circuit appeals court to order an emergency stay.
Several counties have announced that, if Judge Walker lifts the stay, they are ready to begin issuing licenses and performing civil ceremonies for same-sex couples.
And, here’s the Olson/Boies motion to stay:
Prop. 8 Plaintiffs Opp to Motion for Stay