Can someone tell me what "tend to err..." means?

Here's part of the conversation I heard it from :

It's only a matter of time before my security gets through. You should know their policy tends to err
on the side of shoot now, ask later.
"to err on the side of" = display more, rather than less, of (a specified quality) in one’s actions.

They are erring on the side of caution in the face of possible aggression. They are tending to shoot first and ask questions afterwards.
"To err on the side of" also implies displaying a bit too much of that quality in one's actions. ("Err" is related to the word "error"--mistake.)