I see this coming up over and over again in forums, so here’s what to do when you see boot-time icons on a Mac:
Flashing question mark in a folder icon: Your Mac can’t find the boot disk it’s used to. Turn your Mac off and on again, but this time hold down the Option key (Alt on some keyboards) as soon as the Mac starts. You should then see a list of possible boot disks. Lift your finger from the Option key, then select the boot drive from the list using the cursor keys, before hitting Enter to select it. When you boot to OS X, open System Preferences, click Startup Disk, select your boot disk, and click the Restart button.
No Entry symbol/“No” icon/Prohibition icon: Something’s gone wrong and your Mac simply can’t boot. It might be that a bodged update has happened, or you might be suffering a boot disk failure. Whatever the suspected cause try the steps in the entry above — reboot holding down Option and see if you can select a boot drive. If this doesn’t work you may need to boot to the Recovery System. Good luck!
[Update Needed] with an icon of a person and a question mark: The drive you’re attempting to boot from is encrypted and needs unlocking. It might be that FileVault has been set on the drive. You might see this if you’re attempting to boot from a recovery partition on an external USB/Firewire/Thunderbolt drive, for example. Obviously, you’ll need to type the encryption phrase. There’s no way of asking for a passphrase hint here, so if you’ve forgotten it then you’re in trouble. There’s simply no way of unlocking the disk without it (unless you have friends at the CIA/MI5).
Flashing globe icon: For some reason your Mac is attempting to boot from the network (a.k.a. NetBoot). It might do this if it can’t find the correct boot drive. You might see the flashing question mark icon appear immediately after the flashing globe. Whatever the case the instructions to fix things are as described in the first entry above – hold down Option/Alt and then select the boot disk in System Preferences. Note that a globe icon can also indicate Internet Recovery is taking place, although you’ll see a message beneath the icon telling you this.