Matter Manipulation is (as the name implies) the ability to manipulate matter, the physical substance that makes up everything.
Due to everything in the observable universe being made of matter, those with this ability essentially can change anything or even disassemble matter for one shot capability. These particles act as the building blocks for physical matter as well as the bonds between them for a variety of applications. These can range from the spontaneous creation of matter, the conversion of one type of matter into another, causing molecules to produce heat or even render physical durability irrelevant by manipulating the molecules that make up the target
During her concert and subsequent battle with her siblings, the energy Vanya generated also somehow altered the color of her clothing and her violin, turning them both white. She did the same to her civilian wear in an alternate 1963 after accidentally destroying the floor of a building she was being interrogated in by the FBI. She was also able to lighten the color of her skin, making her look ghastly, as well widening the pupils of her eyes. This ability also causes an aura of pure white and blue colors to glow around Vanya.
Lila is able to mimic the powers of the Umbrella Academy, at least while in close proximity to them and typically use these powers with great skill, besting their original owners in combat with ease. Lila was able to copy Vanya's power to absorb, redirect and focus sound and convert it into powerful blasts of energy. As seen where she first harvested the energy Vanya released to annihilate the Temps Commission army and redirect it against the Umbrella Academy. While using this ability, her skin became white and there was a blue aura around her chest.