Foam rolling is a common form of self-myofascial release which is a manual therapy. It is often used by lots of athletes prior to a workout with a view to improving flexibility or after a workout with a view to reducing muscle soreness and promoting quicker recovery.
Pre exercise foam rolling has been found to increase range of movement in the short term.
Post exercise it has been found to help with soreness and fatigue during exercise.
What needs to be expanded on however is finding the optimal duration of foam rolling as there is currently no gold standard foam rolling programme.
For further information on this you can have a look at the below articles.
Ajimsha, M. S., Al-Mudahka, N. R., & Al-Madzhar, J. A. (2015). Effectiveness of myofascial release: Systematic review of randomized controlled trials. Journal of bodywork and movement therapies, 19(1), 102-112.
Andersen, L. L., Jay, K., Andersen, C. H., Jakobsen, M. D., Sundstrup, E., Topp, R., & Behm, D. G. (2013). Acute effects of massage or active exercise in relieving muscle soreness: Randomized controlled trial. The Journal of Strength & Conditioning Research, 27(12), 3352-3359.