Answer:   Permission set is also very similar to profile. Whatever you can manage at profiles (Like Object permissions, Field Permissions, User permissions, Tab settings, App settings, Apex class permission, visualforce permission) the same you can manage here also.
But the main difference between these two is that user can have only one profile and can have multiple permission sets at time.
Example: To give additional permissions to few users who belongs to different profiles over Apps, Tabs, sObjects and fields.