What does "no clean" solder actually mean?
Soldering requires flux to dissolve oxides and to promote wetting. Rosin (made from tree sap) is one  flux material that has long been popular, and comes in various strengths- RMA (Rosin Mildly Activated) or RA (Rosin Activated). Kester says you can leave the flux on the board under fairly benign conditions and experience bears that out (it only becomes active = corrosive) at elevated temperatures, however most manufacturers will clean the board for cosmetic reasons and to allow inspection. Cleaning often involves the use of petroleum solvents- for example by vapor degreasing or just scrubbing. 

Aqueous clean fluxes have been developed that can be cleaned without solvents- using just hot water and detergent. 

No clean fluxes allegedly don't need to be cleaned and can be left on the board, however many of us have had problems with no-clean processes having relatively conductive residue. The residue is ironically extremely hard to remove, much more difficult than the two above-mentioned processes, more like 'can't clean'. Think twice about this kind of flux if you're thinking of sensitive analog boards that have high impedances. Even circuits you may not think of as being analog such as RTCC chips with an external crystal may be affected.  

Safest for sensitive boards is rosin flux followed by a thorough cleaning process.