As an updating addendum to YviDe's answer:
While still very far from being completely understood fecal matter transplants are more than just the commensal bacteria that are beneficial to gut health and able to "just outcompete" Clostridium difficile (CD).
Humans are not only human dna-derived cells and many many bacteria. One part often overlooked is that the human microbiome is also populated with a an abundance of viruses that are surprisingly beneficial for the host's health.
Healthy subjects may be hosts to viruses that not only eat away the food of CD or produce substances that are a bit harmful to CD's metabolism. A healthy gut contains some viruses called bacteriophages that actively seek and destroy CD.
Bacteriophage transfer during faecal microbiota transplantation in Clostridium difficile infection is associated with treatment outcome:
Results: Subjects with CDI demonstrated a significantly higher abundance of bacteriophage Caudovirales and a lower Caudovirales diversity, richness and evenness compared with healthy household controls. Significant correlations were observed between bacterial families Proteobacteria, Actinobacteria and Caudovirales taxa in CDI. FMT treatment resulted in a significant decrease in the abundance of Caudovirales in CDI. Cure after FMT was observed when donor-derived Caudovirales contigs occupied a larger fraction of the enteric virome in the recipients (p=0.024). In treatment responders, FMT was associated with alterations in the virome and the bacterial microbiome, while vancomycin treatment led to alterations in the bacterial community alone.
Conclusions: In a preliminary study, CDI is characterised by enteric virome dysbiosis. Treatment response in FMT was associated with a high colonisation level of donor-derived Caudovirales taxa in the recipient. Caudovirales bacteriophages may play a role in the efficacy of FMT in CDI.
Faecal microbiota transplantation (FMT) is highly effective for the treatment of recurrent Clostridium difficile infection (CDI).
Studies have shown bacterial colonisation after FMT, but data on viral alterations in CDI and the association between viral colonisation and treatment outcome are largely unknown.
CDI was characterised by a high abundance of Caudovirales bacteriophages and a low Caudovirales diversity, richness and evenness compared with healthy household controls.
Donor-derived Caudovirales taxa occupied a significantly larger fraction of the enteric virome in CDI subjects who responded to FMT compared with those who did not.
FMT was associated with alterations in the enteric virome and bacterial microbiome, while vancomycin treatment was associated with alterations of the bacterial microbiome only.
Recipients infused with donor faeces consisting of a higher richness of Caudovirales than that of recipient were all cured with FMT. CDI subjects who had restoration of bacteria community only were found to have disease recurrence.
The restoration of virome community is as important as that of bacterial microbiome in FMT.
Donor selection based on virome characteristics should be considered in FMT practice.
This means that the explanation models given in the first answer are not wrong, but likely incomplete.
Bacteriophage and bacteriocin typing scheme for Clostridium difficile.
Prevention of Clostridium difficile -induced ileocecitis with Bacteriophage(Hamster model)
Molecular Characterization of a Clostridium difficile Bacteriophage and Its Cloned Biologically Active Endolysin
Genomic Organization and Molecular Characterization of Clostridium difficile Bacteriophage ΦCD119