Okay, well for ages we've been on a reasonably good internet plan, which is on ADSL with connection speeds of 1500K/256K and shaping speeds of 128K/128K.
My dad wants to upgrade to an ADSL2+ plan, which gives us the same uploads in the month, but the shaping speeds are 1Mbps/1Mbps.

Now, I am a complete dunce when it comes to the internet, so what does this mean for the connection speeds? And how much faster would that actually make our internet?

So, I guess I just want to know what would change if we upgraded our internet plan.

Any help is greatly appreciated.
"Shaping speeds"? Do you mean at peak times traffic is managed to these speeds? Or is it permanent?

Anyway, with a higher upload speed, you will notice increased responsiveness of webpage loading, lower ping times, uploading files is faster (obviously); generally a better experience.
I can take a road that'll see me through.