You went above the call of duty Tenno. The skill you displayed will inspire your fellow warriors. Wear this, so that they will know what has been achieved here today.
The holographic interface on this emblem will update to display the rank achieved through exemplary dedication to Tactical Alerts.
The Stratos Emblem (also known as a Tactical Specialist Emblem) is a special badge awarded when completing a Stratos Challenge during Tactical Alert missions.
Unlike previous event-exclusive badges, the Stratos Emblem can be acquired multiple times, which will change the content at the center of the badge based on how many different Stratos Challenges the player has completed. The Stratos Emblem can only be acquired once per Tactical Alert.
Before Hotfix 14.10.2, the Stratos Emblem used Arabic numerals (1, 2, 3, etc...).
The Stratos Emblem was designed by Junior Concept Artist Janice Chu. 
The Stratos Emblem once capped at ten levels and would not change further even if another Stratos Emblem was obtained. It is speculated that this was due to a lack of art implementation. This was fixed in the Black Seed Scourge Tactical Alert, which introduced badge levels 11 to 14 to the game, and can be unlocked upon completing the Alert.
Eight Stratos Emblem levels were awarded during the Snowday Showdown event for conclave during Winter Solstice 2016 event. These were later revoked from all participating players via a script on January 9th, 2017, following player feedback.
If logging in when the previous Warframe used is equipped with the Stratos Emblem, the numeral on the badge may show up as "0" on the log-in screen.
Should you manage to enter a Round 1 Tactical Alert after you completed Round 2, you will not be awarded the Stance mod again, but you "rank up" your Stratos Emblem instead.
As of Hotfix 18.4.12 if you move your camera to the other side of the market or codex display in the Liset, the rank markings of the Stratos Emblem will be drawn in front of the display. This is also an easy way to check your rank if you have a visually cluttered Warframe.