The / (slash) and ' (apostrophe) keys are shortcuts to open the Quick Find bar. You can also configure Firefox to automatically search for text when you type any characters outside of a text field. When typing in a text field these characters should show up in the text field and not trigger the Quick Find bar.
If the Quick Find bar opens when you're trying to type in a text field, here are some things you can try:
If you have the most recent version of Firefox, but are still having this problem, here are some things you can try to avoid the problem:
"Search for text when I start typing"
This setting is unchecked by default. If this setting is checked, any character you type in a text field can trigger this issue. In some cases disabling this setting will prevent this issue from reoccurring. If you're having this issue, make sure this setting is unchecked:
Click the menu button
and choose Options.Preferences.
Select the Advanced panel.
The General tab should be displayed, if not, click on it to select it.
In the Accessibility section, make sure Search for text when I start typing is unchecked
Open and close a dialog window
For many people there is no need to restart Firefox to be able to type in text fields again.
Open any Firefox dialog window
For instance, open the download window.
Close the window right away, there's no need to click on anything first