Blue Diamond is one of the member of The Diamond Authority, and one of the four leaders of Homeworld, and of Gem kind. She is also considered the second-oldest of the Diamonds, only younger than White Diamond.
Physical appearance
As one of the Diamonds, she stands very tall when compared to other Gems, dwarfing any other Gem in size with the exception of White Diamond. Her complexion is sky blue, and she has long, straight alice blue hair which curls inward at the ends. Two noticeable and symmetrical locks of her hair curl and point inwards towards her face just below her cheekbones. She has a long ovoid face, a full upper lip, and a straight nose. She also possesses large, sad, downward-slanting eyes—similar to a stereotypical flapper from 1920s, when slanted, soulful-looking eye makeup was very popular. Her irises are light blue with black diamond-shaped pupils, thin arching eyebrows, and three triangular black "eyelashes" under each eye.
Prior to Season 4, Blue Diamond had a darker cloak covering most of her body, and when it's not covering her head, her hair was shown to only grow to the back of her neck, much like Blue Pearl.
Personality
Amongst all the Diamonds, Blue Diamond is shown to be the most sympathetic, and even willing to welcome Sapphire and Lapis Lazuli back to Homeworld after joining the Crystal Gems. She is a calm and collected individual, as she is in charge of the Homeworld's diplomatic structure. This same sympathy also shows towards Steven in particular, even when she's aware of his mother's involvement in the Gem War, saying it wouldn't be right to blame him over something his mother did and she doesn't place any blame on him, even after finding out about Pink Diamond's shattering. And as for members of her court, she doesn't really enjoy changing their positions, as she kept Sapphire and Lapis's places open despite being gone for thousands of years.
There is some indication that suggests Blue was less compassionate prior to the Gem War, as she was angry towards Ruby for fusing with her Sapphire. However, she had changed from this not too long after Sapphire fled, blaming only herself for making her court member run away from her, and her compassionate starting from here.
When she discovered what truly happened to Pink Diamond, Blue became the most affected by the news, and shown a depression side to her, the Diamond unable to fully recover as quickly as Yellow and White. This also makes Blue Diamond a more determined individual to finding out the truth, and even willing to defy White Diamond for the Crystal Gems' safety and well-being. When finding out about her resurrection, Blue Diamond has shown extreme anger towards White, and lost her trust in her altogether, staying behind to save Pink Diamond as everyone else fled.
Abilities
Emotional Aura
Whether this is an intentional power or a side-effect of her own emotion, Blue Diamond is shown to emit a sort of blue aura around her, which causes others around her to share in her emotions, notably sad ones, and "cry her tears". This usually happens when Blue Diamond's emotions start to go awry.
Gem reading
Unlike Yellow Diamond, and possibly the other Diamonds, Blue Diamond is capable of reading the energy off of a individual Gem, and therefore distinguishing one Gem from another. This can also tell her when a being is Half Gem, such as Steven Universe, and exactly how much Gem DNA is in a being, as with Earthstone.
Aura beams
As a more offensive move, Blue diamond is capable of releasing a magical aura blast from her hands, in similar manor to that of numerous laser beams if she needs to.