Empathy is a fundamental ingredient of any psychotherapy treatment. It is so important in TEAM-CBT that it gets its own letter in the acronym: The 'E' in TEAM actually refers to the phase of treatment when offering and receiving empathy is the main goal. In my experience, it is a necessary - although most often not sufficient - element for successful therapy.
Through empathy, the therapist attempts to develop a deeper understanding of the client's idiosyncratic experiences in certain situations. That hinges on the therapist's ability to put themselves in the place of the client, reflecting the client's thought processes and feelings, acknowledging the client's strengths and struggles, and sharing, in a professional manner, the impact that these aspects have had on them, the therapist. With clear communication and a genuine desire to connect, empathy builds a sense of shared experience that allows the therapeutic alliance to flourish.
Empathy is not sympathy, though. Empathy is a process where two people meet at the same level. In sympathy, one 'stronger' player attempts to rescue the 'weaker' one, often times by minimizing their experience in a well-meaning maneuver to quickly sweep away negative feelings. Renowned researcher Dr. Brene Brown has developed a short video that illustrates this distinction. It's well worth three minutes of your time: