royalty-free: Streem doesn't have to pay the user to display the content they upload back to them from our authorized clients (web, desktop, mobile).
perpetual: The right to display the content doesn't expire after some time, unless the account is closed and data is deleted as described in the second paragraph.
irrevocable: Once the user uploads content, they can't tell Streem that they take back the right to display the content, except by deleting the content, which is covered in the second paragraph.
non-exclusive: This is there for the user's benefit. It means that the user retains the right to the content they uploaded, and we don't take exclusive rights on displaying it back to them. So they have full rights to upload/store/do whatever with it elsewhere.
worldwide: These rights are not restricted to a specific country/zone, like the US, because our service operates and displays content around the world.
publicly perform, publicly display: Users can generate public links to their files, so we have to cover the case where they post it publicly and let their content be publicly displayed via the link they created. Publicly display covers still work like images; publicly perform covers "moving" work like music and videos.
derivative works, copies: Gives Streem access to make thumbnails/cover arts (derivative work) and copies of the data (redundant storage).
authorizing others to do so: Lets Streem pass the content through different layers and service providers during the upload, processing, and when data is requested. For example, Streem has to pass the content through a CDN when the user accesses it, which this gives us the right to do.
The main thing that prevents Streem from abusing these policies is the "for use in connection with the Service and Company’s (and its successors’ and affiliates’) business" line. This ensures that we can only operate on the data to provide our service to the user when they authorize us to do so (i.e. if they click the "Share" button, they authorize us to operate on the file to enable it for sharing), and not for something like advertising the user's content to generate money since they haven't authorized us to do that (we'd have to add an opt-in "Advertise this for me" button or add it in to the TOS and appropriately notify everyone if we wanted to be malicious like that, which would be ridiculous for us).
Other cloud storage companies also have very similar TOS's, although they're more colloquial in their wording, so they may be easier to understand, but no different in the rights they're asking for.
If you want a more credible source, take a look at Yishan Wong's (CEO of Reddit) post: http://www.reddit.com/r/blog/comments/1sndxe/weve_rewritten_...