Yes, it is possible to replace parts of a wood floor. Depending on the type of wood and how the floor was originally installed, you can remove and replace damaged sections without having to replace the entire floor. If the existing flooring is hardwood, it can often be sanded and refinished to mask any damage. Laminate flooring can usually be removed and replaced in sections as long as the pattern and colour match.
If the floor was installed with nails, the new pieces should also be nailed into place. If glue is used, you can use a solvent to dissolve the bonding agent and then firmly press the new piece into place.