As Zotero is a desktop software, it stores files, such as article PDFs, directly on your computer. However, if you need to access your Zotero data from multiple computers, you will need to use file syncing. Zotero allows web-based file syncing up to 300mb using Zotero Web, but if you are storing a lot of files you should turn off web syncing, as this allowance will run out.
If you need to use Zotero's syncing features to manage a lot of files whilst working across multiple sites, you can transfer your Zotero data using another method, such as by using a cloud storage service (Dropbox, Google Drive, OneDrive, etc.), but there are significant risks and limitations to this approach. The safest method is to change the Linked Attachment Base Directory, so you care able to store attachment files in an externally linked folder, so that links are functional on two computers. Instructions on how to do this, and other options for file syncing, can be found on Zotero's support site here.
Be sure to frequently back-up your Zotero library when doing this, as there are some risks and limitations to alternative file syncing solutions.