Both phospholipids and triglycerides have an glycerol group to which their other functional groups are attached, but where triglycerides have three fatty acid chains bonded to the glycerol, phospholipids replace one of the fatty acid chains with a phosphate group. This has significant chemical repercussions, with phospholipids being both polar at their phosphate group and non-polar at their fatty acids. Both types of lipid are very important in biological systems; phospholipids in particular are the main structural element in cell membranes.
Triglycerides compose both animal and plant fats and oils and are the main type of energy storage for many types of organisms, along with having various uses in insulating against extreme temperatures. The main difference between fats and oils is simply melting temperature, with oils being liquid at room temperature and fats being solid at room temperature. Many waxes are also triglycerides, with the only real difference being that they are even more solid than fats at normal temperatures.
Phospholipids are ubiquitous in life because of their role in cell membranes, forming bilayers with their hydrophilic phosphorus group ends facing both the exterior and interior of the cells and their hydrophobic fatty acid chains facing each other. Phospholipids in aqueous solutions spontaneously form similar structures when agitated.