Google Analytics . What is a length of visit and depth of visit?

Defination :

*Length of Visit: amount of time spend on a site during a visit.
*Depth of Visit: amount of pages viewed on a site during a visit.

You can easily track both of these metrics for your site (and various visitor segments) with a web analytics package such as Google Analytics (which is free). Install and configuration for basic use is very straightforward.

Length and depth of visit are two useful metrics to track but aren't generally goals in themselves. I would rather someone paid a short visit to my site and filled out a contact form than have them interact with it for an hour and leave without me ever knowing who they were.

You need to carefully define the purpose of your site and figure out what a successful visitor interaction (goal) is. This could be:
A sale.
A capture of contact info.
A white paper download.
A signup or account creation.

Analytics packages allow you to define and demarcate these critical goals and the funnels or paths that lead to them through your site. This allows you to fine-tune the process from first contact to the generation of new or repeat business.