RankNet was originally developed using neural nets, but the underlying model can be different and is not constrained to just neural nets. The cost function for RankNet aims to minimize the number of inversions in ranking. Here an inversion means an incorrect order among a pair of results, i.e. when we rank a lower rated result above a higher rated result in a ranked list. RankNet optimizes the cost function using Stochastic Gradient Descent.
RankNet is a pairwise Laerning to Rank Algorithm
Other pairwise Laerning to Rank Techniques are LambdaMART, LambdaRank
Pairwise approaches work better in practice than pointwise approaches because predicting relative order is closer to the nature of ranking than predicting class label or relevance score