postgis – How to only query data within bounding box?

I have a SELECT query which is taking way too long. The datasets are quite large, around 500MB. I only need to query data within a very specific and small bounding box (map tiles). My current statement seems to select all data from the whole dataset for each tile!

I would like to add perhaps a ST_INTERSECTION and/or ST_INTERSECTS in order to only select a very small part of the data, but not sure if this is the right approach?

I have a statement that looks like this. Part of it is generated through other software (Mapnik), so I can only control the (SELECT * FROM file_wgdqwhafsbynudutfpdz) part of the statement.

SELECT ST_AsBinary("the_geom_3857") AS geom 
FROM (SELECT * FROM file_wgdqwhafsbynudutfpdz) as sub 
WHERE "the_geom_3857" && ST_SetSRID('BOX3D(270052.0209315277 3364987.296198315,270357.7690446685 3365293.044311455)'::box3d, 3857)

How can I make sure I only query the data that I need, ie. within the bounding box, by changing the (SELECT * FROM file_wgdqwhafsbynudutfpdz) part of the statement?

(Also, what does the BOX3D part of the statement actually do?