There are a range of possible applications here, from being an unpaid contributor to an online forum () to caring for a terminally ill relative.A labour of love
Work undertaken for the pleasure of it or for the benefit of a loved one.
But I don't see the relevance of these words:
To my mind, that should not be part of the definition. If it isn't supposed to be (it's hard to tell from your punctuation), maybe you're finding a definition for part of the first definition: 'for someone's benefit'.for someone's benefit, so as to produce a desired effect in another's mind.
In that case, you've chosen a special (and in this case inappropriate) use of 'for someone's benefit'. That expression has two meanings, one literal and one figurative. In the case of caring for an invalid, the carer is doing it 'for the invalid's benefit'; that is the literal meaning. The invalid actually benefits.
The figurative meaning is 'so as to produce a desired effect in another's mind'; here's an example:
'Having dressed for the party, Amanda thought that her blouse was too revealing, so before leaving her bedroom she carefully covered her top with a scarf for her mother's benefit'.
[Her mother didn't actually benefit.]