Copyright strikes can arise for several reasons. If you uploaded content that another publisher owns (such as a video clip or a song clip) without the publisher's permission, they have the right to request that YouTube remove it.
In some cases, YouTube's system will mistakenly remove a video even if you have full rights to it. If you believe you own 100% of the video that was taken down, or if you have written permission to include copyrighted material within the video, you can file a counter notification with YouTube.
Be sure to read the instructions very carefully! Filing a false counter notification can cause your YouTube account to be terminated or even result in legal action against you.
For more information about copyright strikes, YouTube has several articles covering the basics.