The official Snapchat app was developed for Android and mobile iOS operating systems exclusively. However, they also have an API that is able to perform many of the same actions that their app does. UnlockSnapchat.com uses this API in order to view, download and save any Snapchat photos and videos to any device - including PC and Mac.
There are many third party Snapchat apps that you can download to your mobile phone that do these functions but none are available on your computer. There is Snapbox for iOS and SaveMySnap for Android - both of these apps let you log into Snapchat through their apps, in order to send/receive and also store all snaps for that account. They are quite popular but also have their problems.
Mobile apps generally have to store their data in the cloud in order to not fill up your mobile phones hard drive. This leaves them open to account hackings and users can have all of their data leaked. On computers you don't have that issue. You can safely download and use Snapchat on your computer to view snaps and then save them to your Mac or PC.
You can also use UnlockSnapchat to view and browse snaps on your tablet or mobile phone. Just visit the website, enter a Snapchat username and view all of their photo and video history. This is the safest and most secure way to use Snapchat through a browser on any device - including computer.