TL;DR: Just get it, you might need it later.
DigiD is an access verification system common to many Dutch government websites. It is used both for one-factor authentication (user id + password) or for two-factor authentication (user id + password, then a code to be received by SMS and repeated).
Many government services are rendered without involving authenticated access to government websites. Specifically, applying for a BSN, registering home address changes, applying for the 30% tax ruling, and other such procedures don't require it - you download some publicly-available form and mail it; or you must present yourself in some office.
But other government/government-related services do require it - at least for availing yourself of them online. Examples: The Studielink website which allows for enrolling in various educational institutions. The Dutch government portal for information regarding government services, overheid.nl, the "Employee Insurance Agency", UWV, where you apply online for unemployment benefits, etc.
(Even some medical insurance companies are switching their logins to DigiD).
(I don't quite have a good list of examples; you're welcome to edit some into this answer.)
You should probably get it now rather than later, because there's a procedure of sending an authentication code to your registered address, i.e. the registration isn't made purely online.
To get your DigiD, go here. It takes a few days for them to send you an activation code by post, i.e. you don't get the code immediately on registering there.