# to put off what belongs to your former manner of life
"to stop living according to your former manner of life"
# to put off the old man
"to stop living as your former self did"
# old man
The "old man" refers to the "old nature" or "former self". The term "old man" probably refers to the sinful nature with which a person is born. The "new man" is the new nature or new life that God gives a person after they come to believe in Christ.
# that is corrupt because of its deceitful desires
Paul speaks of the sinful human nature as if it were a dead body falling apart in its grave.