This answer is going to pretty much be a summary of a recent article in Archaeology magazine on Hadrian’s Wall

Hadrian’s initial plans to build a wall came out of a few places. First, Hadrian wanted to end Trajan’s policy of extreme expansion, which meant pulling back forces to defendable boundaries. However, there was no natural boundary like a river or ocean for the British colony, so Hadrian planned to build one. A wall was also a clear symbol of the empire’s power- many Roman emperors, including Hadrian, funded massive building projects as a symbol of their authority.

One purpose is obvious- there were troublesome tribes to the north, so the Roman empire wanted to build a wall to keep them out. However, the wall served multiple purposes. As the wall spanned 73 miles, the entire length of the island, it demarcated the boundary between Roman lands and barbarian lands in a way that a natural landmark would in an area without any such natural landmarks. Because the Romans controlled this wall, they were able to use it in several other ways. It kept the people of the empire in the wall, preventing criminals from running away. Being able to control who went in and out of the wall gave the Romans strong control over the economy, as they were able to control trade. Also, the actual construction of the wall was a large economic process which provided years of work for thousands of bored soldiers, which prevented unrest and stimulated the economy.

The Antonine wall was built for a similar reason, but done more poorly. After Hadrian’s death, Antoninus Pius reinvaded Scotland, and then tried to build his own wall for similar reasons to Hadrian. However, this northern frontier was overextended and the troops were needed elsewhere, so Marcus Aurelius pulled back to Hadrian’s wall.

"The Wall at the End of the Empire: The long and varied history of life along Hadrian's Wall" by Jarrett A. Lobell