Non-invasive sampling means that you collect a biological sample from an animal without actually handling the animal. Traditionally, if you wanted to collect samples from animals for f. ex. DNA analysis, you had to catch the animal in a trap and possibly anaesthetise it to be able to take a blood or tissue sample. This type of handling poses a lot of stress on the animal, which in some circumstances may mean that the animal dies.
Non-invasive sampling tries to avoid this stress by setting up for example hair-traps that are only checked every 2 weeks or by collecting fecal samples so that the animals never have to come into direct contact with humans.