A noun formed from a verb by the addition of -ing.
The English gerund is a noun which is derived from a verb by the addition of the suffix -ing:
Talking takes up too much oxygen.
Running is great exercise.
I love cooking.
The English gerund is identical in form to the present participle. The distinction is solely one of usage: the present participle is what is used in the progressive aspect (I am running) and as an adjective (the running total), while the gerund refers to using the -ing form as a noun (running is great exercise).
In the OED, gerunds are called verbal nouns.
Of the following three examples, only the second is a gerund, because they are shoes for running. The other two are participles.
- I am running scared.
- I have running shoes.
- I hear running water.