Real Dictionary

gerund
countable noun: A gerund is a noun formed from a verb which refers to an action, process, or state. In English, gerunds end in '-ing', for example ' running' and ' thinking'.

gerund in American English
in Latin, a verbal noun in the singular of all cases but the nominative, used to indicate continuing or generalized action (Ex.: probandi in onus probandi, “the burden of proving”)
noun: a form regularly derived from a verb and functioning as a noun, having in Latin all case forms but the nominative, as Latin dicendī gen., dicendō, dat., abl., etc., “ saying”

gerund in British English
noun: a noun formed from a verb, denoting an action or state. In English, the gerund, like the present participle, is formed in -ing