There are many kinds of archives and each archive is likely to collect or acquire different materials. In general, archives take in material that has historical value and is relevant to specific collecting areas or organizations.
Archives may describe what is relevant through a collecting policy, a mission statement, or donation and/or transfer guidelines.
Transfers occur when materials go into an archive from within it's parent organization as part of a retention and disposition schedule. Organizations (including universities) may have formal records retention schedules that require certain materials be transferred to the organization's archives once inactive. Organizational archives may also be interested in materials not on the records retention schedule, so it's always a good idea to check with the archives before disposing of anything that might have historical value.
Donations occur when material is given to an archive voluntarily and without compensation. Donations form the bulk of collections for many archives unaffiliated with an academic institution or corporation. Institutional and corporate archives may also have donated portions of their collections, usually pertaining to the parent organization or specific subject areas.