For example a small rise in temperature causes hot dry brush to ignite or a small rise in water level causes a dam to collapse.
Such events are usually very hard to reverse.
One climate-related tipping mentioned is the collapse of the Amazon rainforest into a drier savannah ecosystem. The forest in Brazil may be approaching this fate. See this MSN report. Once this happens there is not enough rain to regrow the forest. Are the forests in Guyana changing to savannah?
Other tipping points concerns the melting of ice in the Artic and Antartic. Once the ice melts the exposed land absorbs the energy of the sun better and warms faster. See this BBC report.
Other tipping points concern the release of methane from melting permafrost in the Artic and from frozen deposits below cold seas. Methane accelerates global warming.