There are several descriptions of what Remez is in Jewish hermeneutics as a hint of something more. The way that Jesus and the apostles use it is to tie scripture to scripture by the use of the same words or ideas.
For a completely fabricated example, if scripture said that Moses drank his coffee hot, then anywhere that coffee was mentioned it would be assumed to be hot, unless otherwise stated. The effect of Remez is to pull all references of coffee together like transparencies so that there was only one cup of coffee.
When Jesus quotes a verse of scripture from the cross, Remez says that he is pulling the whole context of that verse to the cross.