According to Wikipedia, Inbound marketing is a marketing strategy that focuses on getting found by customers.The opposite to Inbound Marketing is traditional marketing (outbound marketing) that focuses on finding customers by building brand awareness through advertising and promotion. In contrast to "permission marketing," a pejorative term for this type of marketing is "interruption marketing."
Getting found by customers is related to relationship marketing and Seth Godin's idea of permission marketing. In his book, The New Rules of Marketing David Meerman Scott recommends that marketers "earn their way in" (via publishing helpful information on a blog etc.) in contrast to outbound marketing where they used to have to "buy, beg, or bug their way in" (via paid advertisements, issuing press releases in the hope they get picked up by the trade press, or paying commissioned sales people, respectively).
In 2006, Brian Halligan and Dharmesh Shah, two MIT MBA graduates, coined the term and started HubSpot as an Inbound Marketing software company. Since then, Inbound Marketing is used by HubSpot and its thousands of customers to get found online. In 2010, Halligan and Shah published their first copy of Inbound Marketing: Get Found Using Google, Social Media, and Blogs.
Lead Generation Systems
Inbound Marketing is a lead generation system. There are many different lead generation systems including: Email marketing, networking, cold calling, referrals, SEM/paid search, SEO, blogging, social media and website. What makes Inbound Marketing effective, and the genius of Halligan and Shah, is that Inbound Marketing is a system for lead generation systems.
Inbound Marketing
Inbound Marketing consists of many different sub-systems including blogging, social media marketing, search engine optimization, offers and landing pages, email marketing and lead nurturing. Each of these systems is simple enough on its own. 
It doesn't take much to start a blog and start publishing content. Almost everyone has or will join a social network. There are many different newsletter and email marketing providers. However, how can you put all these systems together in order to create an effective lead generation strategy? Inbound Marketing has systems to: Get Found, Convert, and Analyze.
Get Found: Getting More Qualified Traffic to Your Website
The Get Found system consists of 3 subsystems: Create, Optimize, and Promote.
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t the core of Inbound Marketing is remarkable digital content (such as videos, whitepaper, articles, slideshows, etc.) that is enticing and interesting to your "marketing persona". In addition to creating remarkable content, Inbound Marketing involves optimizing the content for search engines, and promoting the content in social media. These are the basics of "getting found" online, or driving qualified visitors to your website.
Convert: Converting Visitors into Leads
Once you have more visitors to your website, how can you turn them into leads? A lead is a site visitor who is interested in the products or services you offer. A lead can also be at a different stage of the purchasing cycle (or sales funnel).
To capture leads at different stages of the sales pipeline, you can provide offers that work for the different stages of the funnel. For example, someone at the "top of the funnel" might be interested in general information about an industry subject; while someone at the "bottom of the funnel" might be ready to be contacted.
Converting site visitors into leads require creating enticing and interesting offers to different leads, and capturing the visitor's information by requesting the visitor to fill out a form in exchage for the offer (e.g., participate in a contest to win an iPad).
Convert: Converting Leads into Customers
A site visitor might give out his information in order to receive an offer, but he might not be ready to buy (i.e., he is at the top or middle of the Sales Funnel). However, when this leads become ready, how can you make sure you are at the top of their mind? You can do that with Lead Nurturing and Email Marketing; another Inbound Marketing strategy.
Analyze: Analyze and Innovate
Once you create and implement an Inbound Marketing strategy, how would you know if it is working or not? The beauty of Inbound Marketing that you can quantify most of your work. You can measure the traffic to your website and how much it is increasing, you can measure how many leads you get through your website and what is the conversion rate for the different campaigns.