It depends on what you mean by "banking"
(1) The first form of "banking" was in the financing of trade. This was at least as early as the Greek empire in Europe
http://www.unescap.org/tid/publication/c...
Without this sort of banking, significant international trade is impossible.
(2) Then there is the notion of a bank that takes deposits and uses those deposits to make loans.
http://en.wikipedia.org/wiki/Bank
To the extent that such a bank transforms maturities - lets depositors have their money bank at short notice while making long term (i.e. illiquid loans)
http://en.wikipedia.org/wiki/Asset_liabi...
it has the properties that it:
- provides more long term investment capital than would otherwise be available in an economy, thus enabling faster economic growth;
- is in an inherently dangerous position as it is always subjects to runs - more than the expected number of depositors wanting their money back.
http://rajivsethi.blogspot.com/2009/11/william-dudley-and-hyman-minsky-on.html
http://delong.typepad.com/sdj/2010/03/the-maturity-transformation-and-liquidity-transformation-and-safety-transformation-industtry.html
(3) Note that there are non-banks who also perform maturity transformations - borrowing on the short term market and lending on the long term market. To economists, these are also "banks" - as the term "shadow banking system" suggests.
http://en.wikipedia.org/wiki/Shadow_banking_system
(4) Then there is pure investment banking - the underwriting of securities
http://en.wikipedia.org/wiki/Investment_banking
Without investment banking, government and corporations could not borrow money. Some would consider this an advantage, others a disadvantage.
etc.
It makes it easier and safer than carrying cash around.
I suppose a disadvantage could be if you have an account that charges monthly fees.
