Hello Arthur,
I do not understand exactly what do you want.
If you want erase background and leave object you can use Background Remover and save result in PNG format (not JPEG, BMP, etc).
PNG (portable graphic format) supports transparency feature unlike JPG, BMP, so when you saved result in PNG you do not lost any mask information.
If you want to replace background you can make the following:
1. Open an image with object (for example bird image)
2. Using Background Remover extract it
3. Save Result as PNG file (File->Save Copy As) and choose PNG form "Save as type" list.
4. Copy extracted bird using "Edit->Copy" command.
5. Open an image with new background (for example)
6. Paste copied image as new layer
7. Using "Pick" tool adjust size and position for copied bird.
8. Save collage as file
IMPORTANT: if you save it as JPEG or BMP file PSP merges all layers together you lost possibility edit size and position of bird.
If you want to edit collage in future, save it as PSP file.
Regrds, Dmitry