This page contains information regarding Star Trek: Lower Decks, and thus may contain spoilers.
(covers information from several alternate timelines)
The USS Enterprise-E was equipped with these pods. When the ship traveled back in time from 2373 to 2063 to stop the Borg from altering Earth's history, the ship was boarded by Borg drones, forcing Captain Jean-Luc Picard to set the Enterprise to self-destruct. As a result, all crew were ordered to abandon the ship in these escape pods. The pods landed at various remote points on 21st century Earth, where Picard hoped the crew would "stay out of history's way." One of the pods had the designation H-47.
Fortunately, the Borg were defeated without the need to destroy the Enterprise-E, and the crew – along with the escape pods – were returned to the ship before it journeyed back to the 24th century. (Star Trek: First Contact)
List of escape pods
The numbers of the known escape pods were either seen on an okudagram or on the pods as the vessels departed the Enterprise. The Star Trek Fact Files had an illustration of H-95, and the Star Trek Encyclopedia (4th ed., vol. 1, p. 251) had a dorsal profile, ventral profile, and side profile of H-101.
The script for Star Trek: First Contact called for a scene where the crew was ordered to leave the Enterprise-E by way of the escape pods, something that was not seen earlier. Unbeknown to each other, both John Eaves (tasked by Herman Zimmerman) and Alex Jaeger (he being tasked by his supervisor, Jeff Mann) started design on the shape and launch sequence in the opening months of 1996.  "Lifeboats were never used on the last Enterprise, but this time a number of them are jettisoned from the ship when Picard orders the evacuation," said Jaeger. "They had been incorporated into the ship design–as triangular shapes on the hull–but we had to determine whether those shapes represented some kind of a hatch covering a lifeboat or the actual exterior surface of the lifeboat itself. We went with the latter idea, with the exterior surface serving as a kind of reentry heat shield." (Cinefex, issue 69, p. 116) The producers decided upon Jaeger's approach in April 1996. Eaves, who originally started out from a "grenade" style form, came up with a design that was remarkably similar to Jaeger's, but with a covering hatch. Eaves remarked, "I liked the the beauty and simplicity of Alex's creations, and how he utilized the top of the pod as a heat shield for planetary re-entry." (Star Trek: The Next Generation Sketchbook: The Movies, p. 114) It was further theorized by Jaeger that the pods were automated and had parachutes for landing. 
On a later occasion, Jaeger returned the compliment to Eaves and elaborated further on his thought processes by noting, "I personally like the depth and detail in your version, I wasn't thinking too much of giving the people much room to move, just enough space for a couple of seats ala apollo capsule. Part of the idea of using the outer 'door' as the heat shield came from the look of the exterior panels which you had already done nicely and just for the speed of exit. You don't want to get stuck if the exterior door panel on your pod doesn't work! Also out of VFX simplicity, we didn't want hundreds of door panels flying around banging into the pods etc… Therefore the simple solution of using that outer panel as the heat shield. Also I just loved the idea that even though you've left the E behind, you still bring a piece of her with you." 
Study and CGI model
Once the design was approved, ILM's Bill George built a study model, needed as reference and texture extraction for modeler Michael Bauer, who built and mapped the CGI model. Animation and lighting of the model was done by Habib Zargarpour. "Having used Dynamation for awhile, I figured there had to be a way to extract the motion data from a pod and calculate its acceleration," Zargarpour observed, on the choreographed movements of the flotilla of pods leaving the ship. "After establishing the position and direction of the retros, we could then figure out which thruster groups would be firing at any given time to change the lifeboat's attitude. I did some R&D, a lot of math, and wound up with fully automatic retrorocket animation on each pod, using Dynamation software." (Cinefex, issue 69, pp. 116-117) The ice crystal particles and the gaps left on the hull of the Enterprise-E were added digitally.
Aside from the Sovereign-class, Jaeger also intended his escape pod design to be in use on the four ship classes he designed for Star Trek: First Contact, especially the Akira-class, "You’ll also notice that the Akira class utilizes the escape pods from the Sovereign Class, but the panel details more like the Galaxy class. That’s because I imagined this ship was commissioned right before the “E” and served as a testbed for the new escape pods." In 2001, Foundation Imaging's modeler, Robert Bonchune, paid subtle homage to Alex Jaeger's design as he modeled the Sovereign-type escape pod hatches onto the alternate timeline version of the CGI model for the Nova-class. "I also tried to tie it in to the Enterprise-E (or a Standard Starship) in some ways," stated Bonchune, "in terms of smoothness and escape hatches, intercoolers etc."