Accompany and Escort generally mean to go along with someone( or something ). However there is a little difference.

To Accompany is to go along as an associate on equal terms ( like with a friend or colleague ). Hence, it is used more in informal situations.
I’ll be going to accompany my friend on his shopping trip.

To Escort is to accompany in order to protect, honor or show courtesy. This makes it to be used more in formal situations.
Kindly escort the visiting dignitaries.