Why does DMSO help facilitate halohydrin reactions?
Alkenes predominantly gives relevant 1,2-dihalo product when reacted with a halogen (e.g., $\ce{Br2}$) in a organic solvent such as chloroform or dichliromethane. If the reaction is performed in water, the product is the corresponding 1,2-halohydrin due to restriction applied by polar water molecules caging $\ce{Br-}$ ion. Organic molecules are sparingly soluble in water as solvent. Thus, the halohydrin reaction is often done in a mixture of organic solvent and water. For example, bromohydrin can be achieved by using N-bromosuccinimide as the electrophilic bromine source in $\ce{DMSO/H2O}$.

Use of $\ce{DMSO/H2O}$ as a solvent has few advantages: 


The bromine source, N-bromosuccinimide (NBS) is readily soluble in this solvent system [Ref. 1]).
$\ce{DMSO}$ is also participated in reaction mechanism. Reference 1 has detailed labeling procedure using $\ce{DMSO^{18}}$ to show that isotopic $\ce{^{18}OH}$ was incorporated in $\ce{OH}$ group of bromohydrin [Ref. 1].
Evedence also suggest the participation of water in the medium, probably due to increasd basic nature of water in $\ce{DMSO}$ ($\mathrm{p}K_\mathrm{a}$ of water in $\ce{DMSO}$ is $31.4$ at $\pu{25 ^\circ C}$ [Ref. 2]).


Suggested mechanism for involvement of $\ce{DMSO}$ as follows:



References:


Bromohydrin Formation in Dimethyl Sulfoxide: D. R. Dalton, V. P. Dutta, D. C. Jones , J. Am. Chem. Soc., 1968, 90(20), 5498–5501 (https://pubs.acs.org/doi/abs/10.1021/ja01022a030).
Acidities of water and simple alcohols in dimethyl sulfoxide solution: W. N. Olmstead, Z. Margolin, F. G. Bordwell, J. Org. Chem., 1980, 45(16), 3295–3299 (https://pubs.acs.org/doi/abs/10.1021/jo01304a032).