I've used a similar web site service to transfer images in the past (Dropbox) but recently a client asked me to transmit images using WeTransfer. Ever since then, I've been using it regularly and find it a much simpler, no hassle and effective way to do the same thing. The service is free as long as the upload involves a total of less than 2 GB (that's a lot of files/images, even high res). but you can always sign up for a cost based option that allows you to transfer more GBs. So far, I haven't had a reason to use anything but the free version.
OK, so how do you do it? First, google WeTransfer or go to www.wetransfer.com. Once you're on the site, you'll see a box on the left side (you may have to skip an ad to sign up for their cost-based service).