Hi Shujaath,
There are basically three options if you are integrating local AD with Office 365:
1. Configure DirSync wihtout synchronizing passwords. You will then need to distribute separate password to each user for their Office 365 Service. You get the first temporary password when assigning the license to the user. The User then sets the personal password on first logon.
2. Configure DirSync with password synchronization. The AD password is then synchronized to Office 365, and the user will use the same password for the local AD as for accessing Office 365.
3. Set up Single Sign-on (ADFS). No passwords are synchronized, but all login attempts to Office 365 are instead redirected to the on-premise AD when the user authenticates. Only the local AD password is used.
Regarding step 1 and 2 - you make this option when you are configuring DirSync.
technet.microsoft.com/.../hh967642
technet.microsoft.com/.../jj151786
Hope this helps.