It was customary for the Jews to dance when they were very happy. The abstract nouns "mourning" and "dancing" can be stated as verbs. AT: "You have caused me to stop mourning and to dance with joy instead" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
The writer speaks of gladness as if it were a garment that he could put on. AT: "caused me to be glad" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Here "my glory" refers to the writer's soul or heart or inner being. This represents the entire person of the writer, who worships God because God has made him glad. AT: "I will sing praise to you" (See: [[rc://en/ta/man/translate/figs-synecdoche]])