A locutionary act, or a locutionary speech act in JL Austin’s definition, is the part of an utterance which is the thing which is actually being said. In other words one can define as a locutionary act as the act of producing sounds that have meaning. Meaning is key here do explain Austin’s idea and to give examples, since a parakeet which calls “it is raining”, for example, does not perform a locutionary act since it does not understand the meaning of the utterance.
Good examples for sentences which are locutionary acts are any utterances which simply contain a meaningful statement about objects. For example: “the baby is crying” or “the sky is blue”. Other examples of locutionary acts can help us understand them is linguistic terms of meaning and reference. Such example sentences include: “there is a dog over there” or “Jack loves Jill”. Once again, in order to give a good example of a locutionary act you need to simply thing of a sentence that has meaning, and it is the meaning part of that sentence which is locutionary.