From OpenCog

A LocalQuoteLink is similar to QuoteLink but only affects the direct child, not its descendants. It has the same effect as wrapping the atom with a QuoteLink and each of its outgoing set with an UnquoteLink.

In practice LocalQuoteLink tends to be used only to tell the pattern matcher to interpret root NotLink, OrLink or AndLink literally, as opposed to logic connectors for building negation, disjunction or conjunction of patterns.

Note that LocalQuoteLink can only take effect if its quotation level is zero (see QuoteLink to learn about quotation level), and if it is not locally quoted.