Moving multiple messages to another folder from a list of search results is super easy and fast. You just need to do a couple more clicks than the "Move To" option elsewhere in Gmail:
- Select the conversations you want to move from the search results page.
- Apply the LABEL that you want to move the conversations to from the "Label" icon (now they're labeled, but not yet 'moved to' that new 'folder'.)
- Click the "Archive" icon (in the same bar of icons as "Label" above the message list), and you're done.
Don't ask me why Gmail doesn't just put a "Move To" icon above its search results. It would save a lot of headaches! But the directions I just listed are exactly the same process that Gmail uses behind the scenes when you use "Move To" anywhere else in Gmail. Every time you move a message from, say, the Inbox to another so-called 'folder', all that happens is Gmail adds the desired label and removes the 'Inbox' label. "Archiving" simply removes a message from 'Inbox' without moving it to 'Trash'.
See others' posts above for a more thorough explanation of why/how this isworks. Gmail's 'folders' arearen't actually folders--it all works with labels. Even the Inbox is just a label, the one that Gmail 'opens to' when signing in; it's the label that Gmail applies by default to incoming messages.