Unlocked is associated with GSM/UMTS technologies, meaning you could use it with a cellular provider utilizing such a system, such as ATT or T-Mobile in the U.S. for example.
Whether or not a new phone meets your specific needs is somewhat subjective. I also caution you to switch providers just to get a certain handset. It's a better idea to find the carrier that gives you what you need reception/service wise first, than find a handset.
Does "unlocked" mean I can use the phone with Verizon? Is this phone a leap forward such that I should buy it now, should I just wait for the next Verizon Droid (I currently have a LG and contract through June), or wait for iPhone5? I am big on web browsing, taking photos and videos, uploading photos and videos and gaming. I use Google apps for my business.