Size and Surface Area
Cells need oxygen (for aerobic respiration) and nutrients. They also need to excrete waste products like carbon dioxide and urea. Most organisms need to stay roughly the same temperature so exchange heat too.
Smaller animals have a LARGER surface area to volume ratio. For example a mouse has a larger surface area to volume ratio than an elephant.
In single celled organisms these substances can diffuse directly in/out of the cell through the cell surface membrane. However in multicellular organisms this is too slow because some cells are too deep within the body and they dont have a very big surface area for diffusion. So they need exchange organs.
More Size and Surface Area
Size - the smaller the organism the larger the surface area so its easier to lose heat.
Shape - Animals with a compact shape have a small surface area so lose less heat and vice versa.
Animals with a large surface area to volume ratio lose more water so some animals can develop different kidney structure.
Smaller animals living in colder regions lose heat more so have a high metabolic rate to create more heat.
Smaller mammals may have fur or hibernate in the winter
Larger animals living in larger regions find it hard to lose heat so spend lots of time in water, or for example like elephants have adaption like large flat ears.