“I tend to dress a little more conservatively at the office.”
You're talking with some friends about the kind of clothes that you wear to work, versus during your free time, You say this.
I tend to dress a little more conservatively at the office.
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(something) tends to (do something)
You can talk about things that usually or often happen with the phrase "tends to ___":
It tends to rain a lot at this time of year.
Mom tends to forget things unless you remind her a lot.
You can also use "be" plus an adjective after "tends to":
Homes in the southern U.S. tend to be a bit larger than those in the North.
Japanese people tend to be rather reserved.
Dressing "conservatively" means that you wear clothes that:
have an older, more formal style (like a suit and tie for men)
don't display parts of your body like your chest, legs, stomach, or butt
You can also dress "formally", but that's different. People only dress formally on special occasions like ceremonies. A formal dress for a woman is long and expensive. A man who's dressed formally might be wearing a tuxedo.
On the other hand, some people dress "conservatively" every day.
at the office
When you work in an office, you can call your workplace "the office" in casual conversation. You call it "the office" even when the person you're talking with doesn't work with you.
For example, you can say this to a friend:
I have to stop by the office for a few minutes, so I'll meet you at the restaurant at 7:30.
"The office" sounds more natural than "my office" for talking about your workplace.
Within the workplace, "your office" is the specific room that you work in (if you have one; some people work in cubicles or open rooms with other people):
Frank, I'd like to show you something. Can you come by my office?