The dashy symbol thing is just a symbol for DC current.
No, its the symbol for a DC voltage...
As others have said, that's just the symbol for "DC power"
Oooh! Oooh! No one's taken DC resistance yet, so that one's mine!
OP: Does the adapter have a current rating on it? (5V @ 100mA or something like that.) As others have said, with unregulated supplies, the unloaded voltage is higher, and as load is applied, the voltage drops more and more. At a short circuit, it would be 0V. (Until it broke. Well, then it would still be 0V, and would also smell funny.)
The trick with these is to have enough capacity that the load you'll place on it does not bring it below the minimum voltage at which your device can run. If that power adapter can't supply at least 500mA, I wouldn't bother with it for general use. (Some projects can function very well with 100mA or less of supply capacity, but until you know, you should have some wiggle room.)
At 8V, you're not going to damage the barrel jack input on your Arduino, so go ahead and try it. After you have it plugged in, and your project is running, measure the voltage on the Vin pin (which is basically straight from the barrel jack), and also the 5V pin. Make sure the 5V pin measures between 4.5V and just over 5V. Ideally, Vin should be 6.5V or higher. (Higher is good up to about 12V -- which your adapter won't supply, but another might. After 12V, the onboard regulator has to drop a lot of voltage, and will heat up considerably doing so. Not good practice.)
People seem to loathe the idea of running a regulator in that region below its minimum input voltage, but AFAIK, there's no harm in doing so, it just won't be able to regulate the voltage to 5V. So what? The IC doesn't need the input voltage to be 5.00V on-the-dot, nor does it really need to stay within 1% +/- while it's running. Significant (and especially transient) fluctuation isn't good, but hopefully the supply and decoupling caps prevent that anyway. Am I wrong here?