What does the line “and yet a maiden hath no tongue but thought” mean?

When Portia’s father died, he left a strange will. Like a princess in a fairy tale, his beautiful and wealthy daughter is to be given in marriage to any man who can successfully complete a set trial. Each suitor is confronted with three chests: one gold, one silver, and one lead. He is told that one of the three contains Portia’s picture; if he chooses that one, he wins her hand in marriage. If he chooses incorrectly, he must leave her forever.

By the time Portia speaks the line that you’ve quoted — “And yet a maiden hath no tongue but thought” — we’ve seen two unsuccessful suitors come and go. Each time, Portia has carried out her part of the ritual just as her father’s will requires. In neither case did she show any hint of emotion: neither attraction nor dislike. Both times she showed herself meekly ready to marry any man who won her. This is correct maidenly behavior: modest obedience to her father, with no expression of her own feelings or wishes.

But now Bassanio has come to undergo the trial. Portia has fallen in love with him, and she finds herself unable to behave with her usual decorum. She dreads the moment when Bassanio chooses the wrong casket, because then he’ll have to leave and she’ll never see him again. Aching to delay the moment of truth, she starts talking. To her own horror, she finds herself telling him exactly how she feels about him. The words come tumbling out, but at the same time Portia knows that Bassanio may well be shocked and repelled to hear them. She assures him that she understands how a young woman is supposed to behave: that “a maiden hath no tongue but thought” — in other words, a virtuous girl doesn’t speak out loud at all, whatever may be going in inside her head. Yet here she is, pouring out her heart. Her whole speech is a tug-of-war between her effort to behave correctly, and her overwhelming desire to confess her love.

Luckily, Bassanio doesn’t seem to mind. He chooses the correct casket, and he and Portia are united.

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PORTIA
(to BASSANIO) I pray you, tarry. Pause a day or two
Before you hazard, for in choosing wrong
I lose your company. Therefore forbear awhile.
There’s something tells me—but it is not love—
I would not lose you, and you know yourself
Hate counsels not in such a quality.
But lest you should not understand me well—
And yet a maiden hath no tongue but thought—
I would detain you here some month or two
Before you venture for me. I could teach you
How to choose right, but I am then forsworn.
So will I never be. So may you miss me.
But if you do, you’ll make me wish a sin,
That I had been forsworn. Beshrew your eyes,
They have o'erlooked me and divided me.
One half of me is yours, the other half yours—
Mine own, I would say. But if mine, then yours,
And so all yours. Oh, these naughty times
Put bars between the owners and their rights!
And so, though yours, not yours. Prove it so.
Let Fortune go to hell for it, not I.
I speak too long, but ’tis to peize the time,
To eke it and to draw it out in length,
To stay you from election.