Unlicensed microwave means that it operates in one of the commonly used radio frequency bands, which is shared by lots of other consumer devices such as cordless phones, baby monitors and PC cards. Since there's no FCC licensed required, you can buy the product and pop it up on your roof on the day it arrives.
Licensed microwave means that it operates in an exclusively assigned FCC licensed frequency band and in order to install it your vendor needs to licensed your microwave path. The process takes up to 90-days and so instant gratification would not be a feature.
Unlicensed microwave is low in cost but the downside is that it's susceptible to interference, depending on how much congestion there is in the particular frequency band that the product operates in. The choices are 2.4 GHz, 4.9 GHz (public safety band), 5.3-5.8 GHz, 60 GHz and 70 GHz. Of these, you can forget the 2.4 band. It's a nightmare. The 5.8 band is a pretty safe bet for the time being, because it offers more sub channels to mitigate congestion.
I have no trouble recommending 5.8 products, particularly as they're relatively small investments that won't break anyone's budget. Vendors make strong statements, but none will GUARANTEE interference free performance for any length of time. The only exception are the 60 and 70 GHz products, which are absolutely immune from interference, however restricted to path distances of under half a mile.
By contrast, licensed microwave is absolutely immune from interference, however that protection doesn't come cheap. Expect to pay upwards of $30,000 to $50,000 or more for a licensed microwave connection as opposed to about $3,000 to $20,000 for an unlicensed solution.