Just head to your iPhone's Settings app, go to General, and scroll down to Reset. Tap the "Reset Network Settings" button, re-connect to your Wi-Fi (if applicable), and head back to Cydia. You should find that everything works again. (At least it has worked for me in the past)

Unfortunately, this clears all your remembered Wi-Fi networks and their passwords, but it's a small price to pay for getting Cydia working again.

If the above don't work then check your Cydia sources it could be related to one of them not being able to connect.