I have a lot of solid objects that were exposed to the sun for many years and "obviously" they changed their color. I write obviously because I know it empirically and from other people, but what is actually happening in the material? Are the photons from the sun knocking electrons or what is going on at an atomic level? Or is the heat accelerating the oxidation process? Can anyone help me to understand and visualize this phenomenon?
The term "solid objects" is a rather vague definition. I will try to break it down into categories and try to answer individually. But right at the beginning I can tell that the colour change observed in materials is mostly a result of chemical changes induced by UV light from the sun. By chemical changes I mean three main mechanisms; breaking of chemical bonds, formation of radicals or light being a catalyst for certain reactions. The general field that can answer all questions of this sort is called, photochemistry.
Metals: The sunlight alone cannot to much to pure metals. Of course if the metal is painted (like most of the metals we see in our daily life) the pigments in the paint can degrade (change their chemical structure) by the sunlight, which can cause a colour change.
Humans: (assuming that humans are "solid objects") Most humans change colour in the sunlight as a protection mechanism of the body. The UV light is not good for skin (burns the skin) and therefore human skin exposed to sun produces pigments to absorb the light to protect the skin from burning. The produced pigments result in a colour change.
Plastics: Plastics are one of the most drastically effected materials from sunlight. They may not only change colour but also lose some other materials properties, such as elasticity, due to breaking of chemical bonds of polymers via UV light. The effect of sunlight on plastics can be so drastic that it can even cause health concerns. Most beverages kept in plastic bottles have a sticker on them saying "avoid direct sunlight" because the chemical reactions induced by the UV light can cause some toxic components (or photochemical reaction products) to be released into the liquid.
Paper: Paper is made from wood that mainly consists of cellulose. Cellulose is colourless in principle but because of its opacity looks white. Apparently, cellulose in paper can degrade through different chemical reactions (oxidation and interactions with acids in the paper) and change colour. But it is also found that cellulose absorb UV light and therefore degrade. However, the changes in chemical structure of cellulose is only one of the reasons for colour change in paper. Different types of papers contain different impurities (result of less effort in purification), one of the most common being lingin, another constituent of wood. Lingin gives the brownish colour to the newspaper paper and more prone to degradation compared with cellulose, therefore brown paper changes colour faster compared to white paper.
A side note about fabric: Since cellulose is also the main component of cotton which is used a lot in textile production one can also expect that cotton-made clothes being affected by sunlight.
EDITs: After seeing that my answer is appreciated by the community, I have decided to make a little research about the reason for colour change in paper and added my findings to my answer.
I found out that there is at least one scientist who devoted significant amount of his time to understand the colour change in paper. Here is one of his main publications.
Also found out that there is an answer in Chemistry Stackexchange to a similar question.
It is caused by photochemistry
Most "solid objects" contain some dyes or pigments that make them coloured or their core components consist of substances that are coloured. By definition coloured things absorb light. This is the root cause of the photo degradation that results in changes in colour when things are exposed to light.
The cause of colour is the interaction between the photons of sunlight and the electrons in the coloured compound. Some electrons live in molecular orbitals and can be kicked into higher energy orbitals if the right energy photon interacts with them. This creates colour if the absorbed energy is uneven across the spectrum of light. If the absorption is strong across the whole visible spectrum then the material will be grey or black.
What matters for photo degradation is what happens after absorption of the photons. The electrons in the higher energy levels won't stay there. They will decay back to the lower energy state via a range of processes. Sometimes that decay is simple and the electrons go back to the original ground state and don't affect anything else in the substance. But, in many substances, there are low probability routes to dissipate the extra energy that result in some chemical change in the coloured substance. For most dyes and pigments the probability of such transitions is very low otherwise they would be photographic chemicals not dyes or pigments. But the probability of chemical-change inducing pathways is rarely zero. This is the ultimate cause of photo degradation and colour changes when things are exposed to sunlight. When there is a chemical change the new chemical will rarely be the same colour as the original chemical and long exposure to sunlight generates a lot of opportunities for even low probability pathways to occur.
An exacerbating factor with sunlight occurs because sunlight contains a lot of UV light (where photons have more energy than visible light photons). Most chemicals that absorb in the visible will also have significant UV absorption. This creates electrons in even higher energy states. These may have more ways to decay that result in significant chemical changes to the substance. But the mechanism is the same. Energy is absorbed by driving electrons into higher energy states and their decay can happen in ways that cause chemical changes to the substance. Even when those routes causing chemical change have very low probability, the large flux of photons in sunlight can drive a significant amount of chemical change leading to colour changes in the substance.