As per the Fringe Wikia article on the opening sequence, each color indicates a different setting and the words mentioned throughout the title sequence are the particular areas of science that will be looked at during that episode and/or series of episodes sharing an introduction. In addition to this, the text "Observers are here" flashes during every opening sequence except for episodes using the observers opening sequence.
The blue opening sequence is used for every episode in Season 1 and 2 except "Peter", "Over There", and most episodes in season 3. A blue title sequence indicates that the episode takes place in the prime universe.
The red opening sequence is used for the final episodes of season two and episodes in season three. The red sequence indicates that the episode takes place in the alternate universe.
There is also a red/blue opening sequence indicating that part of the episode takes place in each universe.
The amber/yellow opening sequence was used during season four and indicated that the episode took place during an alternate time line.
The "retro" sequence used in Peter and Subject 13 indicates the episode takes place in 1985.
There was also a black and white/monochrome opening sequence used for a single episode - The Day We Died, signalling a dying world in the year 2036.
The Observers opening sequence was used in the episode Letters of Transit and every episode from season five.
In addition to the color of the title sequences, there are also a variety of different fringe sciences mentioned over the title sequence, depending on the season you're watching. For season five, these are not sciences but more... fundamental aspects of being human.
Season One: Psychokineses, Teleportation, Nanotechnology, Artificial Intelligence, Precognition, Dark Matter, Cybernetics, Suspended Animation, Transmogrification
Season Two: Hypnosis, Pyrokinesis, Hive Mind, ESP, Neuroscience, Clairaudience, Cryonics, Parallel Universes, Astral Projection, Protoscience, Mutation, Genetic Engineering
Episodes using the Retro introduction: Personal Computing, Cold Fusion, Cloning, DNA Profiling, Nanotechnology, Invisibility, Genetic Engineering, Laser Surgery, Stealth Technology, In Vitro Fertilization, Virtual Reality
Season Three: Wormholes, Singularity, Speciation, Synesthesia, Transhumanism, Pandemic, Reanimation, Neural Networks, Telepathy, Transcendence, Retrocognition, Biotechnology
The Day We Died introduction: Cellular Rejuvenation, Thought Extraction, Cryptozoology, Neural Partitioning, Brain Porting, Temporal Plasticity, Dual Maternity, Chaos Structure, Clonal Transplantation, Water, Biosuspension, Hope
Season Four: Existence, Quantum Entanglement, Philosopher's Stone, Psychometry, Viral Therapy, Ethereal Plane, Gravitons, Time Paradox, Psychogenesis, Bilocation, Psychic Surgery, Transgenics
Season Five: Community, Joy, Individuality, Education, Imagination, Private Thought, Due Process, Ownership, Free Will, Freedom