Leaflet is for requesting and displaying raster tiles on the client. PostGIS is for storing and managing geo data. Leaflet and PostGIS do not talk to each other

Leaflet is for requesting and displaying raster tiles on the client. PostGIS is for storing and managing geo data. Leaflet and PostGIS do not talk to each other. Inbetween you need a tile renderer (like Mapnik). Leaflet is a great library if you don't need much (use OpenLayers then).