Quote taken from the review (1) (and which is also duplicated in Jacob's 2015 "canonical DMSO" book (2, p. 16)):

There is some evidence to suggest that DMSO can increase diffusion through the stratum corneum by disruption of the barrier function. This probably occurs through aprotic interactions with intercellular lipids and may also include reversible distortion of lipid head groups that produce a more permeable packing arrangement. DMSO may also play a role in partitioning as well by forming solvent microenvironments within the tissue that can effectively extract solute from vehicle. Finally, DMSO can have a profound solubilizing effect on less soluble agents in a variety of vehicles, increasing penetration simply by delivering a higher concentration to the membrane barrier.

alongside with extensive molecular modelling by Gurtovenko in 2007 (3) are both suggesting quick pore formation and expansion alongside with the thinning of cellular membranes:

The reported membrane thinning and, in particular, pore formation provide a credible molecular-level explanation of how DMSO promotes permeation of molecules, particularly those of hydrophilic nature, through lipid membranes as observed experimentally.

From what I understand, DMSO paves the way for bigger molecules, such as steroids, making inner skin layers and underlying tissue reversibly accessible, sometimes even on nanoscale level. For the precise mechanism I think it is worth reading through the entire paper (3).

(1) Capriotti, K.; Capriotti, J. A. The Journal of clinical and aesthetic dermatology 2012, 5 (9), 24. (2) Jacob, S. W.; Jack, C. Dimethyl sulfoxide (DMSO) in trauma and disease; CRC Press, 2015. (3) Gurtovenko, A. A.; Anwar, J. The Journal of Physical Chemistry B 2007, 111 (35), 10453–10460. DOI 10.1021/jp073113e

Quote taken from the review (1) (and which is also duplicated in Jacob's 2015 "canonical DMSO" book (2, p. 16)):

There is some evidence to suggest that DMSO can increase diffusion through the stratum corneum by disruption of the barrier function. This probably occurs through aprotic interactions with intercellular lipids and may also include reversible distortion of lipid head groups that produce a more permeable packing arrangement. DMSO may also play a role in partitioning as well by forming solvent microenvironments within the tissue that can effectively extract solute from vehicle. Finally, DMSO can have a profound solubilizing effect on less soluble agents in a variety of vehicles, increasing penetration simply by delivering a higher concentration to the membrane barrier.

alongside with extensive molecular modelling by Gurtovenko in 2007 (3) are both suggesting quick pore formation and expansion alongside with the thinning of cellular membranes:

The reported membrane thinning and, in particular, pore formation provide a credible molecular-level explanation of how DMSO promotes permeation of molecules, particularly those of hydrophilic nature, through lipid membranes as observed experimentally.

From what I understand, DMSO paves the way for bigger molecules, such as steroids, making inner skin layers and underlying tissue reversibly accessible, sometimes even on nanoscale level. For the precise mechanism I think it is worth reading through the entire paper (3).

(1) Capriotti, K.; Capriotti, J. A. The Journal of clinical and aesthetic dermatology 2012, 5 (9), 24. 
(2) Jacob, S. W.; Jack, C. Dimethyl sulfoxide (DMSO) in trauma and disease; CRC Press, 2015. 
(3) Gurtovenko, A. A.; Anwar, J. The Journal of Physical Chemistry B 2007, 111 (35), 10453–10460. DOI 10.1021/jp073113e