Friis-Christensen and Lassen report a close correspondence in the last 100 years between average Northern Hemisphere temperatures and changes in the length of the solar magnetic cycle. Observations of the sun and a number of solar-type stars suggest the explanation for this correlation. They reveal that (a) changes in the length of the magnetic activity cycle are correlated with changes in the amplitude of surface magnetic activity; (b) the amplitude changes in turn are positively correlated with changes in the sun's brightness. These relationships connect changes in the length of the solar cycle with solar irradiance changes. They supply a physical mechanism for the connection between terrestrial temperatures and the length of the solar cycle reported by Friis-Christensen and Lassen. Application of the same results to the history of solar surface magnetic activity since the Maunder Minimum yields the result that the change in solar irradiance from 1700 to the present could have been as small as 0.1% or as large as 0.7%. The mid-point of that range, a change in solar irradiance of 0.4%, is sufficient to explain all or most of the recovery from the Little Ice Age of the 17th Century and most of the half-degree global warming observed during the last 100 years. Satellite observations of solar irradiance over the 1978-1989 period have revealed a climatically insignificant brightness change of 0.1% over that period. Other stars similar to the sun display climatically significant changes of up to 0.6%, suggesting that at other times or over longer periods of time the sun may also change by larger amounts than were observed from 1978-1989.