I like playing football.

你這個問題比較含糊，不夠具體應該是。play當謂語動詞時，應根據時態和語態來決定用什麼形式。如:play,played,played,plays等。playing是非謂語動詞形式。-ing形式在句中可以當主語、賓語或其它句子成份。Playing football is one of my favorite outside class activities .I like /enjoy playing football.

因為like doing sth=like to do sth,所以根據like doing sth可得出play要加ing。還可以這樣理解:因為like為介詞，介詞後面必須用動詞的ing形式，所以play要加ing。希望你能明白，加油！！！