An artificial soul that takes the form of a small sphere.
Modified Souls are artificially created souls that can be inserted into inanimate objects such as toys, Gigai and Reigai. A modified soul differs from a typical artificial soul in that they are often given more autonomy and freedom of thought and they have special abilities that allow them to fight on par with Hollows, such as increased speed or strength.
Modified souls were originally created under an initiative known as Project Spearhead, which planned to insert Modified Souls into corpses of dead Shinigami in order to both maximize the usefulness of a Shinigami and to increase the number of soldiers available to fight Hollows at any given time. Due to the questionable ethics involved, the creation of mod souls was eventually banned by Soul Society and Modified Souls were ordered to be executed on sight. However, not all modified souls were caught and executed. The most notable exception would be Kon, who currently occupies and protects Ichigo's body while he is in his Shinigami form.
The anime retains the entirety of the manga explanation but adds a few modifications during the Gotei 13 Invading Army arc:
By altering entrances to the Precipice World, Kageroza Inaba was able to create Modified Souls based off of any Shinigami who passed through them. These Modified Souls were then placed into Reigai that were visually identical to the Shinigami the Modified Soul but were given abilities that surpassed that of the original Shinigami. Using these Reigai and Modified souls, Kageroza infiltrates deep into the Gotei 13 and wages war against the captains and commanders there.