Hollow are former Pluses (deceased Human souls) who lose their hearts to despair or regret, or they remain in the Human World for too long. Any spirit who is not guided to Soul Society by a Shinigami via Konsō may eventually turn into a Hollow.
The majority of ghosts peacefully move on to the Soul Society after their deaths. However, some stay in the living world to fulfil certain goals, such as looking after a loved one, protecting a particular location, or pursuing a grudge from beyond the grave. However, with only limited abilities to interact with the living, and by definition tied to their goals, many ghosts find they are unable to cope when their loved ones move on or old enemies forget them. At this point, some will become dangerously obsessed with fulfilling those goals, even if the means to fulfil them renders the soul empty: for example, killing anyone who comes near a loved one in order to keep them from hurting that person. In doing so, the ghost warps into a Hollow and, ironically, often makes the focus of their obsession into their first victim, such as what Orihime Inoue's brother, Sora, does. This can be prevented if a Shinigami gives the soul a Soul Burial before it turns into a Hollow.
The process by which a soul becomes a Hollow usually takes months to years to complete, reflected by the length of the soul's Chain of Fate, which usually resides in the center of their chest, and connects to their bodies, if present. The Chain of Fate slowly corrodes over time, coinciding with the degradation of the soul's ties to the living world. The process can be accelerated under certain conditions, such as being attacked by a Hollow, giving into extreme despair, or using certain spiritual powers. When the chain completely decays, they become a Hollow when a hole opens up on their chest where the chain was attached, signifying they have lost their heart.