What are the icons that appear on the desktop when I download a program?

OK, new to the Mac so please be gentle with me!
I've downloaded some programs on my Macbook Pro.  The .dmg file appears and I click on it to install the program.  However, there is an icon placed on the desktop for the program, as well as it appearing on the launch bar.  What are these icons for, and can I delete them without affecting the program?
Also, I'm trying to install HTC Sync for my phone but when I run the install, I get the message "HTC Sync Manager can't be opened because it is from an unidentified developer.  Your security preferences allow installation of only apps from the Mac App Store and identified developers."  How do I clear this and run the program?
As I say, new to the Mac so be gentle with me.

A tour of Mac basics might be a good idea.

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