Mature, develop, ripen, age are used in reference to living, growing things or to things with latent capacity for betterment and mean to come or cause to come to the state of being fit for use or enjoyment.
When employed with reference to living things or their specific characters, mature stresses fullness of growth and readiness for normal functioning while develop stresses the unfolding of all that is latent and the attainment of the perfection that is appropriate to the species or is possible to the individual and ripen emphasizes the approach to or the attainment of the peak of perfection.
Age may equal mature when it is applied to the young but more often and in other contexts, routinely, it implies approach to the period of decline or decay.
In their extended applications to things with latent capacity for improvement all these terms imply a perfecting with time.
Mature suggests that something not fully formed undergoes completing changes while develop especially applies to the unfolding into full being or effectiveness of something that is potential, latent, or nebulous.
Both ripen and age imply a becoming fit for some use, action, or purpose over a period of time. Distinctively, ripen tends to suggest the addition of desirable qualities while age may suggest the elimination of unwanted qualities but often the two are used without distinction.