What is sealing the edges of this footpath?
Looks like (just dirt actually) asphalt concrete expansion joint material. But it doesn't really matter what it is if it didn't come out a caulking gun. To insert an expansion joint you'd probably have to pull the first row of bricks up.

Google vulkem caulk if you want a way to easily do it and have something that will remain flexible for upwards of 20 years. Read the warning labels. This stuff works really well, which means it's very bad for you.