更 + [adjective] 更 + 喜欢 / 想 / [other verb of liking or wanting] [A] + 比 + [B] + 更 + [adjective]
更 means "even more". It goes before an adjective, or before a verb of liking or wanting, and assumes a standard already set that this one goes past.
今天更冷 only makes sense if yesterday was already cold. That assumption is what separates 更 from 很.
更 is one of the few words allowed before the adjective in a comparison, and it says both sides are high.
他比我高 says he is taller. 他比我更高 says I am tall and he is taller. 很 and 非常 can't take its place.
In a comparison 还 works too, and sounds more surprised. 还 also has a range of other meanings; 更 does not.
更 is one step up; 最 is the top.
更不 works where the negative can be graded, usually with a verb of wanting or liking: 我更不想去了.