I'm not sure if you're interested in all the statistical part of the distribution so I'll keep it simple.
When you have an exponential distribution exponential(lambda) you have the following:
- Expected value E(X) (mean): 1/lambda
- Variance V(X): 1/lambda^2
- Standard Deviation = sqrt(Variance)
Therefore the standard deviation is the same as the mean.
Those are the basics about the exponential distribution.
In your case, you are using an exponential distribution with lambda = 1 which means the mean will also be 1 so, in average, your interarrival time will be 1.
If you had lambda = 2 your average interarrival time would be 1/2 = 0.5.
Hope that helps