I have seen several explanations about the texture coordinate node and have seen some clips that will use this node while creating a texture, but can anyone tell me when do I need to use this node? Do I need to use it when I want to apply texture to objects?
You use a texture coordinate node when the default Normals value isn't the right one. Each node that has a Vector or Normal input has a default value that it uses if nothing is connected to the input.
The texture coordinate node offers a set of alternative texture coordinates that are useful for different purposes; and is often used in combination with a mapping node to modify its output.
If you look at the manual page for the texture coordinate node it will explain what the values of each of its outputs are. If you look at the manual page for individual nodes, such as the Image texture, they will explain what the default is if no input is connected. The image texture, for example uses the UV coordinates.
The usual uses of the texture coordinate node, include making sure that a group of nodes are all operating on the same coordinates.