Bridging Visas are designed to keep you lawful, while you are in Australia but don't have a substantive visa. If you make a substantive visa application from within Australia, you will need a bridging visa if your current visa will expire before your new visa comes into effect. The good news is that most validon-shore visa applications will result in the granting of a bridging visa.
There are some peculiarities around bridging visas, and if you are granted a bridging visa and plan to temporarily depart Australia it is important you understand the mechanism, or discuss this with your registered migration agent for further clarity. Most bridging visas will cease if you leave the country, even if you hold a substantive visa at the same time.
There are several bridging visas, the below is a general summary:
Bridging Visa A
Often granted against a valid on-shore application for a substantive visa. This visa does not allow you to travel.
Bridging Visa B
This is a visa with permission to travel ie. it allows you to leave and return to Australia.
Bridging Visa C
If you validly apply for a substantive visa on-shore, but your current substantive visa has expired, and you hold a bridging visa (not a BVE), you will automatically be applying for a BVC.
Bridging Visa D
Allows you to remain lawful in Australia and make a substantive visa application.
Bridging Visa E
There are many categories of BVE, and this visa is specifically designed to keep you lawful in certain circumstances. Some general circumstances include making arrangements to leave Australia, awaiting the outcome of judicial proceedings, awaiting certain visa decisions, and more.
The above is general information, as everybody's circumstances are different.