In muon-catalyzed fusion, deuterium and tritium nuclei form atoms with muons, which are essentially heavy electrons. The muons orbit very close to the nuclei, shielding the positive charge of the nuclei so the nuclei can move close enough to fuse.
The main problem with muon-catalyzed fusion is that muons are unstable, and hence there needs to be means of producing muons and muons must be arranged to catalyze as many reactions as possible before decaying.