Within the study of linguistics, semantics examines the meaning of words and sentences. A semantic field is thus the range of words that is employed to discuss some common topic. For example, the semantic field for hiking might include words like backpack, incline, terrain, wildlife, navigate, GPS, and boots. These words are not synonymous, but instead refer to the range of concepts that could be employed in a discussion of hiking.
A semantic field is also culturally specific. For example, hikers traversing the icy terrain of Kandersteg, Switzerland might include words like ice axes and locking carabiners in their semantic field for hiking, while those hiking in Death Valley, California might instead include sodium replacements in their own semantic field for this concept. The culture and the context shapes the semantic field of any topic.
A lexeme is often thought of as a word in its most basic form. A lexical field is then the range of words which could apply in a given position of a sentence, each with a slightly different connotation. Consider the following sentence:
On the trail, I met a hiker.
Let's assume the range of possibilities for the word hiker: its lexical field. In this same sentence, we might choose to use the words backpacker, explorer, climber, alpinist, or adventurer. Each of these words conveys a similar meaning to the word hiker; this is a lexical field for that idea.