This phrase is used metaphorically to express being unable to progress in a situation. Every time I suggest new ideas at work, I feel like I'm up against a brick wall.
Pro Tip 2/3
Frustration
It suggests a high level of frustration or feeling stuck with no solution in sight. Negotiating with the other company, we hit a communication impasse - it's like being up against a brick wall.
Pro Tip 3/3
No Obvious Solution
The phrase implies that a solution isn't immediately visible or available. She was up against a brick wall with the legal issues; there seemed to be no way out.