To play online stuff you need to buy PSN. The price has just risen to £20 for 3 months worth or £50 for a year but Argos are still doing it 'cheaper' £15 and £40 respectively.
If you like dabbling in the odd game then the experience can be enhanced by playing multi player. This is more often than not done 'online'. If you like the war games or something like FIFA then you're pretty much knackered if you dont.
By signing up, you usually get 2 weeks worth for nowt so you can trial it but you have to attach a bank account to it. This is easily deleted by going through the settings after activation but for safety sake I would use an empty account or make sure you turn off auto-renew as they'll bump you for £6 or £7 a month to continue.