Basically economic activities mean the activities through which people earn their income.
Now, these activities can be classified in quiet a number of categories.Some of the most prominent ones are:
A] Of Primary sector : Now this sector as you may be knowing consists of people, mainly producers, who produce by exploiting the natural resources.Some examples are farmers engaged in agricultural activities, people engaged with pisciculture (breeding fishes.)
B] Of Secondary Sector: Now this sector includes mainly those people who transform a good from one form to another.They mainly convert raw materials into final goods.For example, making furniture out of wood.
C] Of Tertiary Sector: This sector includes people who provide useful services.Remember services can be 'factor services' (The services given to the producers by people which help them produce some other goods.Like service of a labour in the factories) or non factor services like banking, insurance etc.
All theses are the major heads under which all the economic activities are covered.So,having a clear cut idea of the above mentioned categories will surely help you.