Peak oil means that the rate of production is set to go into permanent decline and the price of oil is set to become extremely volatile, as a cyclical wave of super-spikes to kill off demand lead to sharp recessions and a downward grind in material standards of living.
We just saw the first iteration of this trend in 2008 and 2009.
Trivially true, but not necessarily helpful. No one is suggesting that dwindling oil supply means we'll be going back to pre-industrial technology levels (well, no one sane, at least). The concern is potential economic shocks due to large increases in the relative price of oil and, by extension, oil-derived goods including anything that requires long-distance shipping.
It's a legitimate concern, but probably overblown. With a sufficient range of alternatives, the inevitable price increases are likely to be gradual and steady, giving plenty of time to adjust. Anybody heavily dependent on cheap transportation is probably still screwed in the mid-to-long term, but at least they'll have time to fail gracefully rather than crash and burn overnight.
There is no guarantee that the price increases will be gradual. If exporters of oil all have low time preference (which they do), then plummet could come very suddenly as wells start to go dry with no replacements (eg, an 80% drop off over a ten year period). There is also no guaranteed that we'll be able to find a suitable replacement. Only nuclear has anything close to the EREOI of oil, and nuclear plants takes a lot of time to build.
There is also oil which requires more energy to extract than it contains (beyond which you'd only do it because you need some energy stored in liquid form).
I can't find the reference, but I think there was a French study in the 80's that claimed at $200/barrel it'd be economical to make liquid hydrocarbons for energy using air and nuclear power.
Using the current population numbers always seems odd. At the current population growth rate does that mean we have only some much smaller amount, say 40 years left?