Getting a second nationality or dual citizenship means that you are a recognized citizen of at least two countries. It also means you have the same rights as someone who received their nationality at birth. It gives you the right to live, study and work within your new citizenship country which can offer you and your family many conveniences and a higher quality of life. On a purely practical level, someone with a second nationality has more ease and greater freedom when it comes to international travel.
As far as lifestyle perspectives go, the option of two passports allows someone to retain ties with the country they are from while being an active participant in whatever new country they call home. As a new citizen you also have the right to serve in office, vote in the local election, and take advantage of any social systems that are in place for citizens.
Within the country and even while traveling you will have reduced travel restrictions, for example if you get a Cyprus Citizenship which is part of the European Union then you can travel visa free to all 26 EU states. From a business perspective you will not need a work permit in your new country of citizenship. You will also be able to open bank accounts, set up businesses and partake in the countries economy. Another major advantage is that individuals with dual citizenship can go to University at either country for domestic rates.