A flit is a quick movement. You might flit around a crowded party, greeting everyone briefly with some light-hearted chatter and moving on quickly.
Whether it's used to describe something literal or figurative, flit refers to something fleeting and quick. Flit and fleet are both related to float. Something that floats keeps moving. A smile might flit across your face or a thought may flit into your mind. That means the smile or the thought is there for a second and then gone.