It's essentially a business decision, rather than a security one. The risks from a business perspective are that you lose users from that country, or who are accessing the site from VPNs located in that country, and that, whilst really unlikely, it's theoretically possible for IP assignments to change, meaning that if you didn't keep these blocks maintained and updated with the latest assignments, you might accidentally block legitimate users from target countries, who happen to have been given IPs from a pool previously assigned to a blocked country.
From a security point of view, it can reduce the volume of attacks, and increase the costs to an attacker of targeting your site (since they need to get machines from specific countries, rather than any machines).
It tends to make sense when you have a regionally restricted product - think of shops where goods are only shipped within a specific country, competitions which only accept entries from people in a given region, or systems which work in conjunction with physical businesses which have a limited range (e.g. deliveries to a national chain store, so there would be no way for a user elsewhere to benefit from the service). In those cases, it tends to be easier to justify the risks, since there is no way people from other countries can use the service (and it wouldn't be hard to include neighbouring countries in case of edge cases - a Portuguese business might include Spanish IP ranges, just in case, say).
It makes less sense when you have an information business, or a digital product. In these cases, you might end up getting more unwanted traffic, as people who want to obtain the product resort to VPNs within allowed countries. Think artificial restrictions such as film releases staggered around the world, TV shows with months of delay before being shown outside the country of origin, or game releases.
You can obtain country specific IP lists from sites such as http://www.ipdeny.com/ipblocks/ and then choose whether to use a whitelist approach ("we only deliver to southern Italy, so will only allow Italian and Vatican City IP addresses") or a blacklist approach ("we see lots of attacks from Australia, so will block all Australian IP addresses").
(Please note, all countries are randomly selected and should not be taken as approval or disapproval of given countries.)