Hi,
I've been using UML for about six or so years now, alongside other design and architectural notations. However, by far the most useful is UML. However, UML is not something that you can learn overnight and suddenly become great at, like any specification, the more you know and understand it the more useful it becomes. Back in the early days I had my doubts, basically because I didn't understand it well enough or how it should be applied but now it is used quite extensively in most of my day to day role as a software architect. The level of abstraction used depends upon what I am trying to achieve, the view I am trying to present and its intended audience.
I am a great fan of the UML Distilled book, however, it does have its limitations and should be used in conjunction with other reference books. I hate to say it but UML is only a notation, how it is applied depends upon your knowledge of the development methodology being used.
Why is it better than boxes and arrows? Well, depending upon the audience it might not be but it depends on what you are trying to achieve from the diagram. My path regular comes into contact with off-shore and on-shore developers and UML is a great language bridge in that regardless of where you are born or educated, UML remains the same. The surrounding text may be substantially different - but a picture does paint a thousand words!
Before UML I used SSADM, DFDs, ERDs, flowcharts etc., everyone did them different and each organisation had their own understanding. As a specification, UML (when used by someone who actually knows it) is consistent and cross-organisational.
Regards,