Cataract occurs when the otherwise transparent lens in eye becomes opaque or cloudy. It grows very slowly and does not cause any pain or discomfort in the eye. This is the reason it may remain undiagnosed till the time it actually causes disturbances in vision.
Although there can be other secondary reasons for cataract development in eye, it primarily occurs because of aging process. Both the primary and secondary reasons lead to similar changes in the eye and can affect vision in the following ways:

Reduced sharpness of image due to protein clumping:

The lens in the eye majorly consists of proteins and water. The arrangement of protein is very precise inside the lens so as to allow light to pass through the lens. This facilitates formation of a clear image on the retina. Due to aging, these proteins start clumping together and form a cloud. This cloud significantly reduces the sharpness of image reaching to retina. Initially only a small part of the lens is affected that may or may not cause vision problems. The cloud may grow and becomes dense. This will further restrict the entry of light leading to blurred vision or eventually vision loss.
Protein clumping is by far the most common cause of age related cataract that can make seeing difficult or vision getting dull or blurred.

Yellowish/brownish discoloration of otherwise clear lens:

With age, the vision of the patient may slowly become brownish in color or dull due to coloring of normally clear lens. This process is very slow and may take long. Initially it starts with a small amount of tinting and can go unnoticed as it does not cause much vision problems. But with time, tinting may increase to an extent that can lead to difficulty while reading and performing normal day to day activities. This advanced discoloration of lens can also lead to inability of the person to identify blue and purple shades of color.
Although this leads to vision problems, in this case, tinting basically does not affect the sharpness of image transmitted to retina. It can definitely be a reason of embarrassment among friends when you assume a color to be black but actually it is purple or blue. This is because of decreased contrast sensitivity