"Arrive by 7:00" means "arrive no later than 7:00."
You can arrive at 6:15, 6:45, 6:58, or 7 on the dot but, please, arrive no later than 7:00. Do not arrive at 7:20 or 7:12 or even 7:01.
Although literally "arrive by 7:00" could mean any time before seven, in real life the normal context would be to arrive shortly before 7:00. Something is going to happen at 7:00. If you arrive later than 7:00 you will miss it, so arrive by 7:00. If you arrive earlier than 7:00 you will have to wait. If you arrive a lot earlier than 7:00 nobody will be expecting you yet, so don't do that, either.
To say "arrive at about 7:00" you would say "arrive at about 7:00," "arrive around 7:00," "arrive seven-ish."
Although it means "arrive no later than 7:00" it is not a very strong or strict way to say it. If it is really important to arrive by 7:00 and not a second later, you would add other words to strengthen it--usually giving a reason. "Arrive by 7:00 sharp, we will close the doors at 7:00." "Be sure to arrive by seven, we will not hold the bus for latecomers."