To negotiate is to try to work out an agreement between parties that each want something out of the deal. You might negotiate with your mom — offering to do more chores for a raise in your allowance. Good luck.
Negotiation is all about give and take. Governments are always negotiating with unions, trying to define the terms of new contracts. The government might offer the teachers union a raise, if they agree to work 200 days a year instead of 180. The verb negotiate can also mean to successfully pass through or travel along. You may have to negotiate a hazardous road, or a tricky path through sticker bushes.