All are formulations that you put on the skin and all contain a mixture of oil and water. However, each has a slightly different composition; ointments contain a higher proportion of oil and are greasy compared with lotions, which have more water and are very light on the skin, and creams, which are somewhere in between the two. Ointments can leave marks on clothes which is unappealing to some patients.
One of the functions of the skin is to regulate heat and water loss from our bodies. When creams, lotions or ointments are applied to the skin, the water they contain tends to evaporate, leaving the oil base on the skin. For this reason, creams and ointments are the best for dry hands in winter (lotions can actually dehydrate the skin as the high water content evaporates, drying the skin out).
For normal skin, a cream is appropriate, while for those with sensitive or eczema prone skin, an ointment would be beneficial.