The server location can be very important when targeting specific places, for example if your websites address was “www.mywebsite.co.uk” and your server was located in the UK then you may achieve better results in the UK version of Google.
Having country specific domains can also be important if you are targeting a country whose language may not be in Latin script, such as Chinese or Russian. Another important point to take in would be if you were on a .com domain and your competitor was on a .co.uk domain then it is much more likely that your competitor would appear higher on Google.co.uk and you will appear higher on Google.co.uk. Naturally however you would like to appear higher on .co.uk as it is much more local and more people within the UK will use Google.co.uk.All of this can lead to search engine optimization benefits as you will achieve better local results, so making sure you have the correct domain name can be important to localised search results. If you are wanting to target worldwide however it would be a good idea to have as many domain names as possible for the countries that you are wanting to target, such as .it for Italy, .es for Spain etc.
In conclusion, it is important that you have your site hosted on the domain of where you are targeting to improve your local search results for that country.