Why is trade and specialization important in economics?

Both are important in two unique ways.

We individuals are not self sufficient. This is caused by several natural facts as lack of resources, land blocked scenario, poor infrastructure/technology, lack of investment, inefficient labour, etc. Therefore, we need to exchange goods and services with other countries or import goods with a medium of exchange. That is, we trade.

Now, while trading we choose from which country to import. Definitely we will import the best quality goods from the cheapest source possible. Therefore, exporting countries compete in terms of specialization. Without specialization, they aren't efficient, aren't productive and hence quality of good deteriorates. When quality deteriorates, the demand for the good in international market falls. This lowers terms of trade, ultimately lowering trade balance surplus. Hence, to survive in the international market and to spontaneously trade, specialization is a must.