In PowerBI.com under Datasets in Left side pane click three dots for your dataset and then click SECURITY.
On Row-Level Security page click Create New Role.
Click Continue on warning sign that says if you re-publish this dataset you have to create row level security again.
Create roles as per requirements. In this case I have dataset that has some sales figures for different states across Australia so I am going to create roles for each of those states thereby limiting users to only see the sales data for their state.
Next step is to add users to those roles created above. Select role on left and under Members tab add users by typing in their email address and click Save. Please note you can only add users who have signed up to PowerBI.com before. If you try add users who have not signed up when you save it will give error.
Under Rules tab select table from your dataset and use DAX query to limit access to the rows in that table. Here I am limiting to only those rows in table Sheet1 where State column has value Western Australia. For this post I am keeping it simple but as you can see you can write complex DAX queries to achieve level of security you want.
Once saved next time users of that role access the dashboard they will see the same report with filtered data. Below are the screenshot of the original dashboard and one seen by the user of Western Australia Users role. You may need to download these images and zoom in to be able to see difference in number values for each visuals.