A burning smell coming from your dryer could mean your vent is clogged with lint and keeping air from getting out. This can be a serious fire hazard, so be sure to clean out your vent regularly.
If you smell burning plastic from your dryer, it could be an issue with the cord or plug. If your dryer cord is loose or damaged, the increased power needed to run your dryer can cause the wires to overheat and sometimes even melt the plug and outlet around it.
Regardless of what the issue is, you should always call a professional electrician immediately to inspect the problem so that you are not putting yourself in danger.