It's a good thing newbies have a place to post simple questions!
What is the value of having a local (on your computer) software wallet when exchanges and other acquisition sites such as localbitcoins.com require you to keep your bitcoins in their wallets?
And a follow-on question: can a local wallet coordinate wallets from multiple sites for easy viewing?
With electrum (electrum.org), you don't even need to keep a wallet on your hard drive if you don't want to. Instead, you just have to keep the wallet seed (a set of 12 words) secure. When you open the electrum client, it will give you the option of restoring the wallet from the seed.
For easy viewing of wallet balances, check out btcbalance.net.