What does the number 256 in pairing curve BN256 indicate? There are many pairing based elliptic curves like MNT curves, BN curves, SS curves etc., When we say BN256 curve, what does the number 256 indicate? Is it some group order or number of bits required to represent some group? 
How to figure out number of bits needed for representing each group G1, G2, and GT for curves like MNT224, BN256, SS512 etc.?
It's the size of the prime number of the underlying field in G1, G2 and GT.

In BN256, G1 is $E(\mathrm{GF}(p))$, G2 is a subgroup of $E(\mathrm{GF}(p^{12}))$ (or $E'(\mathrm{GF}(p^{2}))$ when using a twist) and GT is a subgroup of $\mathrm{GF}(p^{12})$.

Elements of G1 requires the same number of bits as $p$ for each elliptic curve point coordinate. Note that not all prime-friendly curves support cofactor 1, which means that in some cases we need a larger prime for a particular group order. (This is not the case in BN curves).

Elements of G2 require the same as $p^{k}$ for each elliptic curve point coordinate, where $k$ is the embedding degree of the curve. When using twists, we can reduce this by 2, 3, 4 ou 6 depending on the curve. BN curves have embedding degree 12 and support sextic twists, so we can use elements with the same size as $p^{12/6} = p^2$.

Elements of GT require the same size as $p^{k}$.