There are several different popup prompts that you might be shown. A common prompt says "YouTube is updating your channel's account" and offers you choices for linking your YouTube channel to a Google+ Page, rather than a Google+ Profile.
So what do the options on the YouTube is updating your channel's account mean? And how do decline the change?
• If you do not want to make any changes to your YouTube channel, click the X in the upper right-hand corner of the popup. This is the only way to dismiss the prompt without linking your YouTube channel to Google+.
• "Keep your YouTube username" creates a Google+ Page with your Google+ username as the title.
This particular option can create confusion, because it sounds like you won't be making any changes to your YouTube account which is currently using your YouTube username. As noted above, the only way to dismiss the popup without linking your YouTube channel to Google+ is by clicking the X in the upper right-hand corner.
• "Choose a better name" creates a Google+ Page with a name of your choice.
This is the best option for linking to Google+ if you do not want to use the same identity on YouTube as you use for your Google+ Profile and other Google products, like your Gmail email account.
Note that Google+ Page names can be changed a limited number of times, so do your best to choose a Page name that you'd be happy to stick with.
• "Use your Google+ profile name" links your YouTube channel to your existing Google+ personal profile.
You will only see this option if you have already created a Google+ Profile.
If you do choose to link your YouTube channel to a Google+ Page, one thing to keep in mind is that you will only have the option to unlink your YouTube channel from the Page for 14 days. After 14 days, the link is permanent. If you aren't sure which option to choose, either click the X in the upper right-hand corner to dismiss the prompt or choose the option to link to your Google+ Profile, which is indefinitely reversible.
Also see: What does it mean when YouTube offers you "New choices for your channel name"?