One of my frustrations with the GBIF portal is that it is hard to drill down and search in a specific area. You have to zoom in and then click for a list of occurrences in the current bounding box of the map. You can't, for example, draw a polygon such as the boundary of a protected area and search within that area.
As a quick and dirty hack I've thrown together a demo of how it would be possible to search GBIF by drawing the search area on a map. Once a shape is drawn, we call GBIF's API to retrieve the first 300 occurrences from that area. The code is here, and below is a live demo (see also http://bl.ocks.org/rdmpage/43073981694598fecab725a16e890d3b).
This demo uses Leaflet.draw to draw shapes, and Wicket to convert the GeoJSON shape to the WKT format required by GBIF's API. I was inspired by the Leaflet.draw plugin with options set demo by d3noob, and used it as a starting point.