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A sign is the basic unit of semiotics that represents something else. It is made up of the signifier and the signified. For example, the word 'tree' is a sign that signifies the concept of a tree.

The signifier is the form that the sign takes; it is the physical manifestation, such as sound, written character, or image. An example is the word 'cat' when written or spoken.

The signified is the concept that the signifier refers to. It is the mental concept or the meaning behind the sign. For instance, the idea of feline-ness that comes to mind when we hear the word 'cat'.

Denotation refers to the literal, dictionary definition of a sign; the explicit or direct meaning. For example, the denotation of 'rose' is a type of flower.

Connotation is the associated or secondary meaning of a sign that carries cultural and emotional associations. For example, the word 'rose' might connote love or romance.

A syntagm is a linear combination of signs that are arranged in a sequence, and their meanings depend on their relationship within that sequence. An example is a sentence where the meaning changes if words are rearranged.

A paradigm is a set of signs from which one can be chosen to replace another, as they are all applicable in the same context. An example is the set of words that can be chosen as synonyms for 'happy' like 'joyful', 'elated', and 'gleeful'.