"Urban Renewal" is a broad term, but in the U.S. it usually refers to government programs, most common in the 1950s and 1960s, in which areas ranging from a couple city blocks to an entire neighborhood were demolished by government agencies and redeveloped from scratch. Usually this was done in the name of clearing "slums" or "blight," but the results were often disastrous. People living in areas slated for Urban Renewal were forcibly removed from their homes, and many low-income and minority communities in particular never recovered. Some of the redevelopment projects have proved successful, but many have fared poorly. They tend to be very disconnected from the fabric of their surrounding cities.
The Strong Towns approach is diametrically opposed to urban renewal. Rather than redevelop a huge area all at once, we think cities should respect the gradual, incremental evolution that happens when neighborhoods are allowed to change more organically. A better way to help a struggling neighborhood is by making many small investments in response to residents' urgent needs, rather than to dramatically redevelop it.
Some Strong Towns posts that you might find relevant and interesting: