Evidence is absolutely vital for building a convincing academic argument. No matter how strong your logic is, no matter how good your writing style, if you make statements without trustworthy evidence to support them, you will undermine your argument.

What your use of evidence should do:

Clearly support the individual points which contribute to your argument
Indicate what other scholars have written or said about your topic – and how their views relate to your argument
Demonstrate different perspectives in the debate/issue you are writing about, but ultimately show that there is stronger evidence to support your argument than the counter-arguments
Show that the topic being discussed is a complex one, and that your argument acknowledges that

What your use of evidence should not do:

Give the impression references are being used for the sake of it
Make you seem biased, or as though you are twisting evidence to fit your purposes
Show no clear link between your argument and the evidence
Undermine or confuse your argument