Circuit elements (or components) are joined together by wires. Where wires from components connect there is a node. Every wire in the circuit is part of some node.
An "element" just means a circuit component, such as a voltage source, current source, resistor, capacitor, or inductor. You can define a node any place two or more such elements join. Sometimes it is convenient to define nodes in the middle of branches because you happen to be interested in finding the potential there. Otherwise such nodes are considered to be "non-essential" nodes, and aren't required for finding the potentials at other "essential" nodes.
The "V" node in the second circuit is an example of a non-essential node. The two resistors (2 and 6 Ohms) comprise a single series branch between nodes V1 and V2. Those resistors could easily be combined into a single 8 Ohm resistor and one could proceed to find the potentials of node V1 and V2 without difficulty (and with one less node equation). The node V was introduced, apparently, because it was desired to find the potential there.