Why bi-convex lens give ignition? Bi-convex is mostly used type of lenses.It can burn paper with help of sunlight.But why? Why bi-convex lens can give ignition when other lenses can't?
 A: It it not essentially true that only a bi-convex lens causes ignition as a plano-convex lens can also do so( although it's easier with a biconvex lens as it has a unique focal point while a Plano convex lean can focus light to more than one point but still it can converge light). To understand why ignition occurs is because these converging lenses focus light from a source ( suppose here the sun) onto a point on paper and increases the intensity( power per unit area) of light on the point so molecules in paper can have enough activation energy to undergo combustion with oxygen in air to ignite.
Thus other lenses that are  not converging like a bi-concave or Plano-concave, they are diverging lenses so they don't focus light at a point rather spread out light so thus only the converging lenses help to ignite Paper etc.

A: Tausif Hossain's answer that any kind of converging lens that is big enough can in principle set fire to paper with sunlight is true.
However, it does help to have a biconvex lens insofar that you can set fire to paper with a biconvex lens of a smaller diameter than you would need than if you had a plano convex lens. 
It may seem that you want a lens with as short a focal length as you can get, to increase the system numerical aperture so that the focal spot will be smaller and thus more intense. However, if you try to increase the optical power of the surfaces (i.e. use smaller radiusses of curvature) too much, you begin to introduce significant spherical aberration and the increasing of optical power becomes counterproductive: spherical aberration spoils the focus more than the increased power will shrink it.
Spherical aberration varies a the fourth power of the optical power for a single surface. Therefore, splitting the wished for optical power between two surfaces can give you the same optical power for less spherical aberration, even though both contribute the same sign of spherical aberration. Therefore, you can achieve a smaller spot than you would for a plano convex lens of the same diameter and focal length.
A: To get "ignition" you need to concentrate the rays from the Sun over a reasonably small area.
A converging lens of any type will do the converging in the focal plane and a short focal length converging lens will produce a small image of the Sun in the focal plane sufficient to get the temperature of the piece of paper located in the focal plane of the lens high enough to ignite the paper.
Increasing the diameter $D$ of the lens will allow more of the rays from the Sun to be concentrated but as you make the focal length of a lens smaller the maximum diameter that the lens can have decreases.

Given that visual angle of the Sun is about $\frac 1 2 ^\circ \approx \frac {1}{100}^{\rm c}$, ie small, the diameter of the Sun's image in the focal plane of the lens, $d$, is approximately $\frac{f}{100}$.
A $5\, \rm cm$ focal length lens will produce an image of the Sun with a diameter of approximately $\frac 1 2 \,\rm mm$.  
A diverging lens by its very nature is unable to concentrate the rays of light from the Sun.
