This may be a run-on sentence, but here goes. It's harder to succinctly describe than it might seem!

Lead Nurturing is the process of developing dialogs between a company and a potential buyer by delivering relevant content and information through various communication channels (marketing automation and personal interactions) in order to help the two parties get connected at the right time and potentially build a relationship.

Here's a link to a resource on Genius.com to help optimizing lead nurturing: http://www.genius.com/resources/MarketingGenius/content/whitepapers/optimizeLeadNurturing/

A marketing process that uses content (offers, tools, whitepapers...) and distribution tactics (email, phone, retargeting...) to engage known prospects over a period of time. Lead nurturing may also involve the use of business logic that tells the marketer what content and distribution tactics to use based on behavior exhibited previously by the prospect.

Sure- it's easy since I wrote one for the new Lead Nurturing Cheat Sheet.

Lead Nurturing: The process of building relationships with qualified prospects regardless of their timing to buy, with the goal of earning their business when they are ready.

You can find the full sheet here (no registration required): http://www.marketo.com/library/LeadNurturing_cheatsheet11_12pm.pdf

For a more detailed response you can check out our 40 Free Wworkbook on Lead Nuturting- viewed over 10K times by B2B marketers (no registration required): http://www.marketo.com/dg2-lead-nurturing

I'll take a shot, trying for "succinct yet thorough" -

Lead Nurturing: The process of engaging prospects by providing the information and dialogue they need at each stage of their buying process to position your company as the best choice to help them achieve their business objectives.

Great question and great answers so far. I would make it a succinct, but thorough definition in 3 parts (see more detailed description here: http://digitalbodylanguage.blogspot.com/2009/06/goals-of-lead-nurturing.html):

Lead nurturing is the discipline of:
1) Maintaining permission to stay in contact, through adding value
2) Establishing key ideas, perspectives, and viewpoints
3) Monitoring for signs of progress through the buying process

Let's borrow a quote from Glengarry Glen Ross (1992)

( lead nurturing is the process to) Get them to sign on the line which is dotted.
Alec Baldwin

We are all guilty of using this key phrase extensively without necessarily agreeing on a single definition. To me, a good lead nurtiring system does not paint with a broad brush and does not put everyone in a "holding tank". Lead nurturing is simply the act of advancing an opportunity at a pace that matches the customers unique situation. Good lead nurturing recognizes what the customer needs to move forward (whether it is time, more information, budget or something outside of his control) and applies that "medicine" at the right time, and in appropriate doses.

Taking a $3.00 lead or a $30.00 warm live transfer it does not matter. Until the applicant refuses or directs you to Stop Calling the lead is LIVE. The problem has been across all lines of business is allowing the TOP producers in Hign closing percentages the RIGHT to vascilate the incoming leads to accomodate their closing numbers.
Steve Tomaszewski
Virtual Agent Services Chicago

A prospect that is less than 10% probability of a sale within 1 month, but may tip to greater than 50% within 6 months with proper follow up with information and continued contact.