Essentially, DMSO offers:
1.) 100% absorption
2.) A "resevoir" of the solute dissolved, inside the skin, prolonging the half life of the solute by weeks
3.) Increased effiacy and uptake of the solute into cells

100% absorption

DMSO 80% gel (15 g, t.i.d.) was completely absorbed within 4 hours after application to the shaved backs of miniature pigs.
https://www.sciencedirect.com/science/article/pii/S0022202X15479436

A "resevoir" of the solute dissolved, inside the skin, prolonging the half life of the solute by weeks

When applied, it reaches the stratum corneum where the solute gets trapped, dispersing into the body over long periods of time

"Within a few minutes after application to the surface of human skin, hydrocortisone and fluocinolone acetonide in the presence of dimethylsulfoxide (DMSO) are established in a protected reservoir in the stratum corneum. This reservoir remains over a 16 day period and is resistant to washing of the skin surface with soap, water, and alcohol"
https://jamanetwork.com/journals/jamadermatology/fullarticle/529213

"After cutaneous application half of the applied dose is eliminated within fourteen days. After intravenous application half of the applied dose is eliminated within eight days.”
https://www.sciencedirect.com/science/article/pii/0002961067901663

"DMSO permeation increases quickly at the beginning of the experiments and results in a steady-state plateau. This observation suggests that DMSO is able to build a reservoir in the skin providing enhanced solubility of E2."
https://pmc.ncbi.nlm.nih.gov/articles/PMC7999216/

In this study, they tested different strengths of Idoxuridine in DMSO on guinea-pig skin and directly measured how much drug stayed trapped in the stratum corneum 2 hours after application. The amount in the reservoir perfectly predicted how well it fought herpes skin infections ( r = 0.95–0.97).

More applications per day built a bigger reservoir and worked better
https://www.sciencedirect.com/science/article/pii/S0022202X87900893

Increased effiacy and uptake of the solute into cells.

DMSO creates water pores in membranes allowing for increased uptake of solutes.

"It is well known that dimethyl sulphoxide (DMSO) increases membrane permeability, which makes it widely used as a vehicle to facilitate drug delivery across biological membranes... The increase in Tl⁺ permeability induced by DMSO was not changed in the presence of blockers for K⁺ channel and Na⁺-K⁺ ATPase, suggesting that Tl⁺ permeates through transient water pores induced by DMSO to enter into the cell,"
https://www.researchgate.net/publication/225093725_Ion_transport_through_dimethyl_sulfoxide_DMSO_induced_transient_water_pores_in_cell_membranes

"...Since DMSO is an excellent solvent for steroids, and since cortisol is the most potent fibroblast inhibitor among the naturally occurring corticosteroids, the next step was to test both of these agents in combination in the tissue culture assay system (FIGURE 6). The concentration of cortisol used was 0.01 pg/ml and DMSO was at 1 per cent. At these concentrations, there was no significant suppression of fibroblast growth by either substance used independently. However, in combination, cortisol at 0.01 pglml plus DMSO at 1% significantly depressed fibroblast growth."

"...These experiments suggest a certain degree of synergism between DMSO and corticosteroids and indicate that DMSO could be an important tool for potentiating the biological effectiveness of steroids at the cellular level."
https://www.ncbi.nlm.nih.gov/pubmed/5232228 (credit to Haidut)