Standard broadband is called ADSL, or ADSL2+ to give it its correct name. With ADSL2+ you'll typically get speeds of up to 16Mbps but depending on how far away you are from the exchange, you could get a much slower connection than that.
With fibre optic broadband, depending on which provider you choose you could get a connection as fast as 152Mbps. How does this make a difference to your browsing? Well, the faster the connection, the quicker things load, like emails, YouTube videos, websites and streaming sites like Netflix.
However, with a faster connection, typically comes a more expensive tariff, which is why it's a good idea to compare providers against each other.