You mean the blow in kind? Where small holes are made at the tops of stud cavities and the material(usually cellulose) is blown into the stud cavity?

Depends on the framing behind the walls. Many old houses had blocking between studs(horizontal 2x4's). That would prevent the material from filling the entire cavity and not be worth the time/expense. Open cavities can be filled and save money versus tearing out the walls(especially old lath and plaster construction), insulating with batts/foam, and sheetrocking.

yes yes and depends
2 posts no info..
new home - existing home
no-one knows how to answer you OP.

The house is an old house built in the 1940's. Someone said that we could drill into the wall and pump material made out of cotton into the cavities - -not from above into the walls from the attic but sideways.

Wonder if it is just a gimmick.

Don't know where you are but up here in the great white north i.e. Canada, we have companies that specialize in doing that. They do not use cotton, but cellulose as handymac mentioned. I had it done to a previous home and it was great, my present home was built in the late 1940's and I would do it again except the builder's installed an early type of batt insulation which prevents me from blowing anything in.
When they insulated my other house, they started by removing a shingle, drilling a 2 inch hole and probing with a "fish" (a flexible metal rod) to find the studs and any blocking , and so on until they had access to the interior of the entire wall. They blew in the insulation, plugged the holes and replaced the shingles and then off to the other walls. Slick !! The only problem with this type of process is that there will be some settling of the insulation over time, the amount of which will depend on the skill of the installer, but in my opinion, it's still a better option than tearing out and replacing wallboard.

So in answer to your question, no , it's not a gimmick !

do you have insulation in the walls at all?

you can check by removing the covers of light
switches (mid wall) and outlet covers (low on walls).
you should be able to see insulation between the
elec box and the wall.
I've used a plastic knife to gently probe around the
sides of the box to 'feel' for insulation. the
serrated part of the plastic knife will snare a few
particles of the insulation so that you can identify
the type of insulation.

if there is no insulation you are a good candidate
for the drilling and blowing of insulation.

batt insulation may have voids and gaps, but you
willnot be able to blow insulation into these type
of walls.

products like cellulose if installed previously
will have settled over the years and filling the
voids at the tops of the cavities may be an option.

let us know what you find.

and we will ask for more details as we go...we are
not being nosey..just trying to get a feel so that
the answers will pertain to your situation.

where are you located?
what type of cladding on the exterior of the
walls, and what is on the interior..sheetrock
paneling??