" To lock up" means to use a key to close the locks on the doors of one's car or home so that other people cannot get in without a key.
You probably lock up your house before you go to sleep at night.
Well, I am locking up my car before I go into the office so no one steals it.
Here I could also just say " lock" - I " lock" my car, but we often say " lock up" (two words) to add more emphasis to the sentence.
After I lock up my car, I walk toward the building. It's a short walk and I'm there in no time.
The phrase " in no time" means very quickly, right away, or with very little delay.
If you listen to ESL Podcast premium courses like this, you'll learn new vocabulary in no time, or very quickly.
When I get to the office building, I take out my badge and put it around my neck.
" To take out" means to remove from something, such as remove it from my briefcase.
A " badge" (badge) is a piece of identification, usually or often with a photograph, that shows that a person works for a specific organization or business.