What do I get by paying more for a bicycle?
With so many good answers I hesitate to say anything.

But, in an effort to add something useful to the conversation...

The Value Curve
Part of the reason it's hard to understand the difference between more and less expensive bikes is that you do get what you pay for, but cost increases faster than value. 

What is Value?
For the purposes of this answer I'm defining "value" as some measurable improvement.
For example, a $15 steel chain that will last 3,000 miles vs an $80.00 stainless steel chain that will last 8,000 miles (made up numbers - this is only an example)

Why is There a Curve?
The cost to manufacture increases faster than value. Each improvement cost more to manufacture than the last one.

For Example
It's easy to see a difference between a $50.00 bike and a $400.00 bike.
It's harder (not impossible) to see the difference between a $800.00 bike and an $1200.00 bike.
As price goes up it gets harder and harder to see an increase in value.

I would argue that at some price point there is no value increase and you are paying (hopefully) for craftsmanship, like extra polish or fancy lug work or exotic materials that are expensive but don't contribute to a measurable difference.



Suppose I agree that there is a value curve - what should I do?
There is a "sweet spot" in the curve. A place where you get the most bang for your buck. The problem is that I can't tell you exactly where that is because it changes over time and it depends on the individual's situation - finances and type of riding.
Bike shoppers have to balance their budget with the desired level of performance and decide where their sweet spot is.  

Always test ride bikes before buying. Always ride more than one so you can compare.
A parking lot is not a great way to compare ride but it's much better than nothing. Bike feel matters.