An activity done on an incidental basis means it happens randomly or casually. The activity would not be the main purpose of your trip. Non Incidental is exactly the opposite and would be pre-planned.
Examples: 'I am going on holiday and may have a go at Scuba Diving whilst I'm out there, if I can find a place that does it.' - That would be participation in an activity on an 'Incidental' basis. 'I am going on a specific Scuba Diving holiday, where my main intention is to Scuba Dive' - That would be participation on a 'Non Incidental' basis.