Export each image from a collection in Google Earth Engine

Export.image.toDrive is a client-side function, and you cannot call it from a server-side function (the one you are mapping over), so you have to do it all in the client side. I have a repo where you can find a bunch of useful functions: https://github.com/fitoprincipe/geetools-code-editor There is a function to export all images from an ImageCollection to the Drive cloud.

var batch = require('users/fitoprincipe/geetools:batch')

// Create a geometry representing an export region.
var roi = ee.Geometry.Rectangle([-63.0, 9.2, -63.1, 9.3]);

// Load the Sentinel-1 ImageCollection.
var sentinel1 = ee.ImageCollection('COPERNICUS/S1_GRD');

// Filter by metadata properties.
var IW_H = sentinel1
  // Filter to get images with VV and VH dual polarization.
  .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))
  .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
  // Filter to get images collected in interferometric wide swath mode.
  .filter(ee.Filter.eq('instrumentMode', 'IW'))
  // Filter IWs to get High res.
  .filter(ee.Filter.eq('resolution', 'H'))
  // Filter IW-Highs to get 10m res
  .filter(ee.Filter.eq('resolution_meters', 10));

// Filter to get images from different look angles 
var DescCollection = IW_H.filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'));

batch.Download.ImageCollection.toDrive(DescCollection, 'Folder', 
                {scale: 10, 
                 region: roi.getInfo()["coordinates"], 
                 type: 'float'})

You can find the complete code in here and the documentation here