An electron transport chain is a series of sequential chemical reactions that carry an electron from a starting point to a final acceptor for reduction. Since you mention ATP synthase, you are talking about the mitochondrial associated electron transport chain called oxidative phosphorylation. In eukaryotic cells, this occurs in the mitochondrial membrane.
The initial stages of glucose metabolism like glycolysis and the citric acid cycle produce electron rich chemical species such as NADH. The NADH donates an electron to the start of oxidative phosphorylation. The electron is passed though a series of five redox reactions where it is passed from one protein complex to another until it finally ends up reducing a molecule of oxygen (O2) to produce a water molecule. Along the way, protons are released to the outside of the membrane, thus setting up a proton gradient with an excess of protons outside of the membrane and a lack of protons inside of the membrane. ATP synthase is an enzyme that spans the membrane and allows the protons to travel along the natural gradient from high concentration to low concentration (from outside the membrane to inside the membrane). As the protons flow through the ATP synthase, they power the enzyme to take an ADP molecule and add an extra phosphate goup to produce ATP, the cell's preferred stored form of chemical energy. This production of ATP via ATP synthase is why the mitochondria is called the powerhouse of the cell.
The hydrogen and electron transport system consists of several hydrogen and electron acceptors. Biological oxidation-reduction reactions involve both hydrogen and electron acceptors. Hydrogen or electrons are passed from one acceptor to another. There are several intermediate hydrogen acceptors, and a final hydrogen acceptor which is molecular oxygen.
At various stages in Glycolysis, Oxidation of pyruvic acid and the Krebs citric acid cycle, removal of hydrogens (2h) takes place. The initial acceptor of hydrogens released from the substrates is NAD, except in one case. This exception is the hydrogens released from succinate. Here the initial acceptor is FAD of flavoprotein.