Those checkered boxes should appear white if you saved it as a jpeg. I think i am a bit confused on what you are actually trying to do? just get an image of the person you cut out with a white background? if that is so, simple make a new layer above your background and paint it white, and then take your cut out image and place it on an additional layer on top of the white layer. But like I said, those checkered boxes should appear white if you were to save it as a jpeg. Let me know if I misunderstood you, ill check back in a bit.
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Okay, I am just going to give you a step by step of how I could cut someone out of a picture, my girlfriend would always want me to cut her out and blend her in with celebrities for jokes.
starting with one background layer---
-drag background layer down to the create new layer to duplicate the layer
-work within the duplicate layer, sometimes you cannot preform certain actions on the main background layer becasue it is locked.
-use the lasso and wrap the person
-once you have a perfect selection of the person, go to the top menu-"Select"->"Inverse
-This will make it so everything except the person is selected.
-use the background eraser tool from the left tool bar, make the area large and make several passes to ensure you have erased everything
-turn visibility of the first main background off
-merge visible
This is as close as you will get.. you cannot save transparent images, like i said before, if you were to have the person cut out with checkered boxes around him/her it means there is absolutely no data or pixels in those checkered areas... so if you were to try to save it as a jpeg, it just fills it in with whitespace... the only reason it allows you to do that in the first place, is so that you can take that person and overlay it on TOP of another layer.. (like i did for the fake picture of my gf hugging chris carrabba) but if i never added her cutout to the chris carrabba photo and i saved it.. it would be a cut-out of her with a bunch of white space around her...
Windows and macs use transparent menus and stuff, but that is because it is constantly being calculated.. the computer says.. okay.. he just dragged a blue box behind the top menu bar, so im going to change that to a grayish blue so that it "appears transparent..
If i misunderstood again, lemme know ill try to help ya out.. maybe you already figured it out by now though
Also clays method of getting rid of the background is much faster than using the background eraser tool. but you still need to lasso your subject