Physical Appearance
Katherine is described as Elena's doppelganger, this is observed by almost every character in the show and even Elena herself. Katherine is described as being very beautiful, slim, and selfish with brown eyes seaking something to quench her thirst. Sometimes Katherine can be seen cool and cold by her appearance. She is portrayed as rather vain about her looks, and has no problem using her beauty to get what she wants. Pearl later reveals that when the vampires were captured in 1864, and a guard let Katherine go free; Pearl tells Damon that,"he was obsessed with her." Stefan said then Katherine does not care about others; she only cares about herself.

Powers and abilities
She has all of the powers and weaknesses of a vampire. According to the novels she was born in 1614 and turned when she was 17 in 1631 but the series will have her born around 1475, about 140 years earlier than the books, making her even more powerful than in the novels.

Transfigured in 1492 unintentionally by Rose (unintentionally on Rose's part), she is as a result much more powerful than the Salvatore Brothers who she turned after she had been a vampire for 372 years but much less so than Pearl was who was turned sometime in the 1430's about sixty years before Katherine. A demonstration of how much more powerful she was than the Salvatore Brothers was when she easily defeated them in two fights with each brother in The Return. Another demonstration of her immense physical strength is when she snapped the iron shackles that Stefan tied her up in as if they were made out of balsa wood and slammed Stefan against the dungeon wall with one hand. In Masquerade she came very close to defeating the brothers simultaneously but would have been killed by Damon while Stefan pinned her down if Jeremy Gilbert hadn't intervened to save Elena. Even then it was mostly luck and some teamwork by the brothers that she almost lost rather than brute strength since Stefan and Damon together are still not as old as Katherine, making them like babies to her.

In addition to her enormous physical strength that improved with age her resistance to magic/psychic phenomena also improves with age and experience. This was demonstrated when she easily resisted the witch Bonnie Bennett's attempt to inflict physical pain within Katherine's head by producing multiple aneurysms in her brain. Earlier, Bonnie had very easily inflicted that very same type of attack on the much younger Damon which had him holding his head and crying out in agony while Bonnie's efforts had no effect on Katherine. (The Return)

Katherine has impressive mental powers of her own. In addition to the usual ability to compel humans all vampires have, she also has the power to get inside the head telepathically of a vampire, at least a relatively weak one like Stefan Salvatore, who in addition to being a much younger vampire, he also didn't partake in drinking human blood regularly (until recently) weakening him further. He probably doesn't practice the vampire arts since he identifies more with humans than vampires so likely his mental powers aren't as well developed compared to a vampire of his age who embraces his nature. Katherine placed dream like images of them in 1864 and a contemporarily dressed Elena Gilbert and Damon Salvatore in his mind as part of her efforts to split up Elena and Stefan and get Stefan back for herself (Memory Lane). It has been stated that the glamor power doesn't have any effect on other supernatural beings like other vampires and werewolves.
The extent of her other powers is unknown but it is easy to assume they have been well honed in the 518 years she has been a vampire. One ability she has honed for the past 146 years is by taking a sip of vervain laced fluids she has developed a immunity to it, which usually weakens a vampire enough so even a human can over power them and a large enough dose can kill them. In 1864, Stefan Salvatore had vervain his system when he was still human. She bit and drank his blood at one time and was greatly weakened, possibly threatening her life. In Memory Lane, she pretended to be greatly weakened by it when Stefan Salvatore injected her with it with a large hypodermic needle and interrogated her, but she was faking in order to have him listen to the story as to why she came back. When the deception no longer served a purpose, she told him on how she was able to resist after snapping the chains that bound her in the dungeon.
However Katherine is extremely weaker than older vampires like Elijah and The Originals.

Also, she possesses a Lapis Lazuli necklace, therefore she can walk in daylight without being harmed like the Salvatore Brothers, Caroline Forbes, Elijah(one of the original vampires) and also Pearl and her daughter Anna when they were alive.