The speaker begins by asking God (along with Jesus and the Holy Ghost; together, they are the Trinity that makes up the Christian "three-personed God") to attack his heart as if it were the gates of a fortress town. The speaker wants God to enter his heart aggressively and violently, instead of gently. Then, in line 5, the speaker explicitly likens himself to a captured town. He tries to let God enter, but has trouble because the speaker's rational side seems to be in control.
At the "turn" of the poem (see the "Form and Meter" section for more on the importance of the sonnet form and, specifically, the "turn"), the speaker admits that he loves God, and wants to be loved, but is tied down to God's unspecified "enemy" instead, whom we can think of as Satan, or possibly "reason." The speaker asks God to break the speaker's ties with the enemy, and to bring the speaker to Him, not letting him go free. He then explains why he wants all of this, reasoning with double meanings: he can't really be free unless God enslaves and excites him, and he can't refrain from sex unless God carries him away and delights him.