Contracts between the original record custodian and FamilySearch govern nearly all of the records within the collections on FamilySearch.
For most contracts, FamilySearch acquires rights for you to use the records merely for incidental, personal, noncommercial genealogical research purposes. This includes the right to extract factual data about your direct family line and then put that data into your personal family tree, which you may then use for your own needs.
Contracts prohibit the publication or distribution of the actual record images or documents (including through print or the web). They also prohibit wholesale indexing, transcribing, or translating of the records, even when these activities are for nonprofit purposes. You must acquire written permission from the custodian of the original records before you publish an image of a record or document.
From the collection screen of the record, click How to Use this Collection to access a wiki article about the collection. Some of these wiki articles indicate who the custodian of the collection is.