In iOS 6, you could tap the Edit button in Messages to delete or forward one or more messages from a text/iMessage conversation. There’s no Edit button in iOS 7’s version of Messages.

Here’s the work around: Tap and hold on any speech bubble in your conversation. A popover menu appears. Tap on the More button, and now you’re in editing mode. You can check as many messages as you’d like with the round checkboxes (checkcircles?) that appear, and then tap either the trash can icon at the bottom left, or the forward button at the bottom right.

There’s also a Delete All button at the upper left to wipe out the entire conversation history from this editing mode.

Source: Mac OSX Hints