Some folks look at me and see a certain swagger, which in Texas is called 'walking.'

Summary

This quote suggests that in Texas, confidence and self-assurance can be commonly perceived as a natural quality called "walking." It implies that the speaker exudes a sense of pride and fearlessness that reflects the Texan way of life. It hints at the fact that in this specific cultural context, displaying a certain level of swagger or self-assured demeanor is seen as normal and socially acceptable.