Tricom badge
The tricom badge was a combination of combadge, holoPADD, tricorder, and portable transporter designed to be worn on a Starfleet uniform. It was in use by the late 32nd century.

Functions on the tricom were activated by hand gestures: 
 A fist and then an upward open palm activated the holoPADD. A tap of the badge deactivated the holoPADD.
 A squeeze and pulling out gesture of the hand activated the tricorder. Reverse movements deactivated the tricorder.
 A single tap on the badge would activate the transporter. A holographic coordinate system would appear, upon which the user would type in their destination. Then, the user would tap the badge and they would be transported.
 A double tap on the badge would activate the home button, which would transport the user back to where they were going.

Along with the many functions listed here, the tricom indicated the rank of the individual, with ranks ranging from crewman to fleet admiral.

Having arrived in 3189,  expressed an interest in Kovich's badge, and promptly broke it under her heel when he allowed her to "play with it." ()

Starfleet Command replaced the 23rd century badges of the  crew with the tricoms. They were trained in how to use the tricoms by Lieutenant Audrey Willa and others. The first gesture taught to them was for activating the holoPADD. While some adjusted to the new badges, others, like Lieutenant junior grade Linus, found the adjustment more difficult. He struggled with the single tap and double tap functions of the badge, finding himself not where he wanted to be. ()

Starfleet Academy cadets had a different version of the tricom badge that omitted the oval backing, with the emblem rendered in three silver shapes, with rank pips denoted by four short bars that protruded from the right side. (DIS: "All Is Possible")

Appendices

Background information

The name of this technology is from Property Master Mario Moreira in the aftershow . He explained in the show how the badge was made in the prop shop and how it works in the Star Trek universe. He worked on the hand gestures, which the actors, like their fictional counterparts, had to learn.

The various ranks on the tricoms were shown in the aftershow.

External link
 

Communications technology
Sensor technology
Computer technology
Transporter technology
Memory Alpha articles named from supplementary resources