1g is a fairly common way of denoting acceleration, particularly in respect to the tolerances of the human body.
On earth 1g is 9.8m/s/s this is the constant aceleraion due to gravity which we all feel all the time, although we don't always interpret this as a force or acceleration as we as used to it so a more useful analogy is that its is the acceleration you feel if you jump off a ledge.
In terms of tolerance and what it 'feels' like a typical car may generate 1g of acceleration under very heavy braking. High performance racing cars may develop maybe 3-5 g as a sustained force.
The most agile fighter jets can sustain perhaps about 10 g in a turn but this is certainly well into the limit of what a fit and conditioned human can tolerate before blacking out.
For impacts 30 g is a generally accepted limit of what is reasonably survivable but there are plenty of incidences of for example F1 drivers surviving 40g+ peak impact forces with few ill effects.