Why is it good for users to have a boost in hash rate?
A higher global hash rate usually means a more secure network (assuming the hardware is not used against the network, of course).
Also, I still don't understand what ASIC is, it's better hardware that's designed specifically for mining bitcoins?
Yes. It is much faster and more power-efficient.
It involves better software too or no?
No, it's a purely hardware thing.
How much faster will it be at mining? Is there some place where I can read lay discussion of this issue, I'm not that technically advanced. Thanks!
https://bitcointalk.org/index.php?topic=87934.0