In a very simplistic way you could say that Yammer is private and Twitter is private. You could also say that Twitter is for the public and individuals while Yammer is for companies. That would not be the most accurate statement as both individuals and companies use Twitter and vice-versa. However if you are a company and want your corporate communications to be private then Yammer is the solution for you.
Yammer

As we all know Twitter is growing at an almost exponential pace. Yammer is growing nicely as well, their site states over 70,000 companies use their service. Each of those companies may have multiple users. They call it “Enterprise Microblogging” as the entire corporate can communicate and collaborate in real time.
Corporate Social Network
As the individuals in your corporate join they create profiles about themselves. This creates a form or company social network. Each profile includes a photo, title, contact info, expertise and background. If you work in a large environment this is an interesting way for individuals to learn about each other. In small startups it is not uncommon to introduce new team members at a weekly or monthly meeting. That allows others to learn a little about each person however any one person would only learn about those joining the company after them. Also, in large companies this would not be practical. The social network that Yammer provides is a good way to allow those in the company learn more about each other and feel more connected.
Yammer makes your organization a better place to work by making it feel smaller, helping people to find and meet each other, and busting silos between groups and departments. Also, because it’s a network, it becomes more powerful the more people that join.
Collaboration Inside and Out
Not only can you communicate privately with those in your company but also those outside that you give permission to. There is an admin account for your corporate Yammer account. Now you can also allow contractors, suppliers, and anyone else you may want in your network to join.
Searching for Knowledge
As with twitter, you can search for keywords. All the information between anyone in the corporate is saved. There may be a past project or any other type of communications you would like to learn more about and can by searching keywords. An amazing ability that we all wish we could do for every spoken word within an organization for various reasons.
Mobile
They also provide the ability for everyone to access in and through Yammer with mobile devices. Without such a feature it would not be any where as near as useful.
Take a look at Yammer to learn more. And by the way, no one asked me to write this.

