There have been many personal experiences documented where people have experienced relief from itching of mosquito bites on the application of their own saliva to the itchy spot (reference 1, reference 2) It helps to reduce the itching because saliva has been proven to speed up tissue repair and has antibacterial properties. It also provides a moisturising effect on the itchy spot (reference). Salt is also known to provide relief to itching (reference) and the slight salt content of saliva helps in that respect too.