3g means, youll connect to the internet by a mobile internet provider, just like you would with an iphone or any kind of smartphone.
you pay for mobile internet from a mobile company/cellphone provider, like verizon in the us or vodaphone/tonline in germany and then get to connect to the internet
usually you get a limit you can surf for, like 1gb at full speed, afterwards you connection speed gets reduced to 64kbit [just like 12 years ago
] which should still suffice to play online... but its a pain to download
pros: you get to go online everywhere your chosen provider has covered, which should be everywhere in towns, many roads, probably not in the mountains... well its different for all of them i guess
con: you have to pay, just like every other cellphone contract. you have to pay for internet twice or even three times, if you happen to own a home connection, a dataplan for your smartphone and a 3g psp vita... so yeah, things can add up really fast.
to be honest, if you have an iphone or any other kind of device with mobile internet, dont pay for 3g
if you dont and like to be online everywhere, you may think about it though.