''Producir'' means to produce, it is the action of generate something. For exaple: Mi negocio produce ropa de algodon (my business produces cotton clothes).
''Producirse'' can be used as Jorge said -to produce yourself, for example: Ella quiere producirse para la fiesta (She wants to get ready or get produced to the party) or you can also use it as a way to say that something occured spontaneously. For example: Los accidentes de auto suelen producirse mayormente los fines de semana (Car accidents tend to happen mostly on weekends)