Loose thread (stripped) tapered bottom bracket frame connection
A video could really help, sounds like the threads of the cups and/or of the frame shell are damaged. Probably the Bottom Bracket cups need to be removed so the threads can be inspected for damage, like rust, or cross-threading, stripped threads etc. If the threads of the shell are in good enough condition, they can be cleaned and a new BB installed. If the threads of the shell are damaged, then it would be a bit more complicated and deserve it's own question/answer.

This image (from Park Tool website) has the names of some BB parts. Even if it's not a perfect match, editing the question and using these terms would make the question clearer.