Largest component in a Biplane is its large wings, normally there are two of them and are called upper-aileron and lower-aileron or one can simply call each of them as wing.
Holding both these wings together are components called "struts" which you can find in this picture below, and "cables" are used to hold the structure around them, while Struts also provide resistance to compression and preventing the upper and lower wings collapsing inwards, and wire braces, providing tensile strength.
Image for reference only
Biplane component names:
• Wings (normally two, interconnected via cables. Called upper-aileron and lower-aileron.)
• Struts (Metal components, holds together the wings, and helps in resistance to compression.)
• Cables (hold the wings and structure around them.)
• Engine components.
• Propellers
• Spinner
• Body structure.
• Front and rear landing wheels.
• Fuselage
• Elevators
• Cockpit