It generally drops as your cardiovascular fitness improves, but I believe it's endurance work, 90+ minutes, that affects the resting rate significantly. Mine dropped over 10 beats (to 48) when I trained for bike centuries & touring.
Don't get too hung up on resting heart rate since genetics is a big factor. It is good to monitor in case it spikes which is an indication of over-training or stress.
The average heart rate is just the average while your timer is on (presumably during a workout). If you're tracking it, turn the timer on after your warm-up & before your cool-down so you get a more meaning full number. I like to track time above, in & below my training zone but average hr is good for steady-state or tempo workouts.
Debra