Closed-back headphones seal the ear cup with a solid outer shell. This creates passive noise isolation — outside sound is blocked from entering, and your audio is contained within the cups. Both effects are valuable in recording environments.
For tracking (recording vocals, instruments, or voice-over while listening to a mix through headphones), closed-back designs are required. Open-back headphones would bleed their audio into the microphone, ruining the recording. The Audio-Technica ATH-M50x and Sony MDR-7506 are the industry standards for this purpose.
Passive noise isolation in closed-back headphones typically ranges from 10 to 32 dB of attenuation depending on the design and fit. The Beyerdynamic DT 770 Pro and Sennheiser HD 280 Pro are at the high end of passive isolation among studio monitors.
The sealed design introduces some acoustic challenges. The cup's resonances can add coloration to the sound — a very slight boominess in the low frequencies and a slightly less natural soundstage compared to open-back designs. Good closed-back headphones are designed to minimize this coloration while maintaining the isolation advantage.