Sometimes technical descriptions are made with technical vocabulary neologisms in order to capture complicated and nuanced concepts which might be ungainly to convey correctly with simpler non-technical terms. So it may be difficult to come up with a description of a technical concept using only non-technical terms.
A rule in a language is context-free if the rule (affecting some words together) does not use text surrounding those words in order to apply correctly.
For example, suppose you want to make a comparative out of an adjective. Just add '-er': hot -> hotter, tall -> taller. For longer words, you use 'more' first: 'more consistent', 'more independent'. And then for a few words, like 'good' you have a rule exception: 'better'. For all of these, it doesn't matter what the word is, you don't need to know anything else in the sentence to form that comparative: in 'he is good' and 'he is better', the comparative doesn't depend on anything else in that sentence outside of what happens to the adjective.
In contrast, one might say that conjugation of verbs is context-sensitive (the alternative to context-free). For example, in the present simple in English, it is 'I say' and 'he says': to get the right ending on the verb, you need to know the context (the pronoun that comes before). The pronoun itself is not part of the thing that changed, but its presence changed the following word.