Finishing a rough-surface wall in bedroom
That wall surface material looks like it is the backing of some older type wall covering that had a mesh material for adding strength or glue retention.
It is also possible that you are looking at the original wall covering itself that may be a straw or grass material that was woven into a mat and then glued to the wall in sheets.
A zoomed in closeup of your picture reveals that the wall covering is a grass or straw material that was woven with thin vertical threads. It is also clear that it was painted over!!

If that mesh material is covered with paint it will be very difficult to remove. If it is not painted over it may just be possible to lightly spray the wall with a mist of hot water from a squirt bottle to see if the old wall covering glue will soften. As it softens you should be able to scrape carefully with a &quot;putty knife&quot; and wipe away the excess glue with a sponge rinsed frequently in warm water.
A painted over surface like that would entail a lot more work. There are several possible alternatives:

Remove the wall materials completely down to the studs and apply a new wall surface using drywall. This will finish down smooth after taping and sanding.
Try installing a new thin layer of drywall over the existing surface. This may require smoothing off any bigger bumps in the old surface. Any electrical switch and outlet openings may require box extensions to be installed. Also if that wall has any windows or door openings there may need to be adjustment of the trim. Going the route leaves you with a fresh new surface to finish similar to the first option.
Another possible scheme is to do some scraping and rough sanding of that existing surface to smooth out any large bumps and then use a skim coat of drywall mud to smooth out the surface. I have used a similar process to smooth out a textured ceiling and wall and found that skimming works best if you take the smoothing in repeated steps of mud application and then sanding and scraping once the mud is dry. A skim coating leaves a relatively soft material on the wall and it is a good idea to come back afterwards and paint it with two to three coats of good quality primer paint.