Meanings
Fig.: to spend less; to be more frugal

Examples
I stopped working full-time and I have to tighten my belt until I find another job
Non lavoro più a tempo pieno e dovrò tirare la cinghia finché non trovo un'altra occupazione

After spending a lot of money on our new house, we'll have to tighten our belts a little if we want to send our son to a good private school
Dopo aver speso tutti quei soldi per la nostra nuova casa, dovremo tirare un po' la cinghia se vogliamo mandare nostro figlio a una buona scuola privat

Belt-tightening is good for citizens but not for members of Congress. In fact, the Senate has made drastic cuts to the State budget yet, as far as it's concerned, it has continued to spend as much, and even more, than before
Tirare la cinghia va bene per i cittadini ma non per i parlamentari: infatti, il Senato ha apportato drastici tagli al bilancio dello Stato ma, per quanto lo riguarda, ha continuato a spendere e spandere come e più di prima

Origin
If you don't eat enough, you will lose weight and will have to pull in your belt