This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Windows tries to protect you by not letting you run random programs downloaded from the Internet without warning you. The program doesn't contain a digital signature, which means that you cannot be sure that the program really comes from who you think it comes.
What the worst consequence can be? That the program is not the real program that you think it is, but instead is a virus or malware made to look like it is from some trustworthy party. If it is a virus or malware, it can in principle do anything, including deleting the entire contents of your harddisk or steal private and personal information about you.
"The publisher could not be verified. Do you want to run it (This file does not have a valid digital signature...)" ?
You can turn this off by right-clicking the EXE and select Properties. At the bottom of the dialog is an Unblock button - click that. I recommend you do that only for apps that you trust. This is a Windows security feature - it tracks where the file originated and if it did not come from your PC (that is, it came from the internet or even from a network drive), it will not run the app without first checking with you (and as Japser mentioned the app might not actually have been started by you and thus could be a virus).