Indemnity is a formal legal term that simply means one person -- the person providing the indemnity assurance -- will pay for legal costs incurred by another person. If you are assigning a copyright to another person, there is little risk to you, the assignor, of legal costs associated with the copyright. So indemnity from the assignee, the person to whom you assign the copyright, is probably not critical. However, the assignee will likely ask you for indemnity, so it is important that you understand the concepts of indemnity even if you don't need to ask for it.
Copyright assignees generally require an indemnity from the assignor. The standard, customary indemnity clause requires the assignor to verify that the copyright being assigned does not violate the copyright of another creative work. For example, the assignor represents that a copyrighted poem is in fact an original work and is not a plagiarized version of another copyrighted work. Under the indemnity clause, the assignor agrees to pay for any costs incurred by the assignee if that representation ever proves untrue.
Indemnity clauses generally cover actual costs incurred by the assignee in defending or paying on a copyright violation claim. For example, if the assignee uses a copyrighted song, and some other artist then sues the assignee because that song plagiarizes a portion of the other artist's song, then the assignee will have an indemnification claim against the assignor. The assignor will, under the indemnity clause, have to pay the assignee's attorney's fees, and will have to pay any settlement or judgement reached in that lawsuit.
From the assignor's perspective, an indemnity clause should not be so broad that it covers all claims, including frivolous claims. For instance, the assignor should negotiate for the indemnity clause to apply only to "judgments" entered against the assignee, and not just "actions" instituted against the assignee. The difference is significant. If the assignor must indemnify for all actions, the assignor will have to pay to defend even frivolous claims. Adding the term "judgments" will limit the assignor's indemnification duties to only those claims that have merit and result in final judgments entered by a judge. It is important make sure that the indemnification only includes actions brought about by the assignor's prior actions so that the assignor is not subject to paying legal fees for the actions of other regarding the copyright.
In rare circumstances, an indemnity from the assignee to the assignor may be important. If the copyright assignment agreement gives the assignee permission to change the copyrighted material and not just use or reproduce it in its original form, then the assignor may want to demand indemnity from the assignee. This type of indemnity is similar to the indemnity that the assignee will want. In this circumstance, the assignor wants assurance that when the assignee changes the copyrighted material, the assignee will not plagiarize any other copyrighted material. If such plagiarism is committed, the assignor wants the same protections that it is giving to the assignee.