Does borax do anything more for "boosting" detergent than adding active oxygen would? Borax, $\ce{Na2B4O7}$, is often marketed as a "laundry booster" under the brand "20 Mule Team Borax".  The unit crystal of borax can be seen below.



Other laundry products in the past have added sodium perborate (which can be produced from borax, hydrogen peroxide, and sodium hydroxide) as a bleaching additive.  The "peroxide" portion can readily be seen below.



Through what mechanism does the plain borax "boost" the detergent?  Would it be more effective to throw some weak peroxide and a small amount of base into the laundry to form the perborate instead of using plain borax?
Borax was used as a "builder" in washing formulations long before perborate was used as a bleach. "Builder" is the terminology for additives which reduce the influence of water hardness. Other examples of builders include trisodium phosphate, soda, polyphosphates (like Graham's salt) or today most often aluminosilicate ion exchangers (Phosphates are more or less forbidden nowadays because of eutrophication of rivers and seas).