"说明自己意图" can be translated into English as "state one's own intentions" or "clarify one's intentions".
"State one's own intentions" emphasizes the act of explicitly expressing or declaring one's plans or purposes.
"Clarify one's intentions" focuses on making one's intentions clear or understandable, especially when they might be ambiguous or misunderstood.
Both expressions are appropriate depending on the context and the desired nuance.