The Roman soldier would have fastened the breastplate around his chest. There were 2 types of breastplates. The first type was made by joining broad metal bands together using leather thongs. The other was made of chain mail. Both types served the same purpose – to protect the soldier’s vital organs.
In Isaiah 59:16-17, the Lord puts on “righteousness as a breastplate,”and then goes to battle.
God offers his own righteousness to every believer in Jesus Christ. Putting on the  breastplate of righteousness means –

Believing in Jesus and his righteousness, not our own. Gal 2:20-21
Standing firm against injustice and corruption. Heb. 1:9
Knowing that God promises his protection against the forces of evil for those
who have faith in Jesus. 2 Thess 3:3

“With the breastplate of righteousness in place.” Eph. 6:14