1. Excessively or foolishly infatuated; obsessed in a silly or irrational way
Usage: informal; usually followed by 'over' or 'about'
2. Senile or mentally confused; having lost mental sharpness, especially due to old age
Usage: informal; sometimes considered mildly offensive

Examples

• She went completely gaga over the new celebrity.
• The fans were gaga about the band's latest album.
• His grandmother is getting a bit gaga in her old age.
• He's gaga for vintage cars and spends all his time restoring them.
• The audience went gaga when the surprise guest appeared on stage.