At Western universities like the University of Redlands, you're expected to acknowledge every contribution that did not originate from you such as ideas, computer code, and media. This approach is based on the Western idea of ownership such that if an idea is considered to be "owned" by Ana Solis, use of her ideas should acknowledge Ana Solis. However, when something is commonly known, believed, or accepted by your audience and not "owned" by anyone or anything (e.g. the sky is blue) you needn't cite it.
As a student, this can be tricky because you're still learning what's foundational, contested, and cutting edge in your discipline. Whether or not someone or something has staked ownership of an idea, concept, or technology may not be clear to you When in doubt, talk with your professor and err on the side of caution by citing a source.
For specifics on when to cite a source, read Warning: When You Must Cite.
To understand how to paraphrase without plagiarizing, read Fair Paraphrase.
[T]he notion of ‘stealing’ another’s work has its origins in the peculiarly Western conjunction between the ‘growth of the notion of human right’ (freedom of speech) and the ‘stress on individual property’ (copyright). -- Guide to Advising International Students about Academic Integrity.
Research involves adding one's ideas to the ideas of others. When you cite the work of others, you not only distinguish your contributions from that of others, you also formally connect your ideas to others. Over time, citations record the dynamic interaction of ideas.
Screenshot taken from Citation: A (Very) Brief Introduction by libncsu
Failing to cite others work is seen -- particularly through Western eyes -- as offensive, unethical, and sometimes illegal.
Screenshot modified from Citation: A (Very) Brief Introduction by libncsu