“Your seal and your cord and your staff that is in your hand.” Tamar was very wise. She knew Judah did not like her and would have liked nothing better than for her to die or somehow be out of his life. So Tamar likely knew that if she showed up pregnant that Judah would order her death, which indeed he did (Gen. 38:24). So she asked that she be given in pledge things that no one could deny belonged to Judah himself: his personal seal, cord, and staff. The seal would have been a ring, stamp, or cylinder on a cord worn around his neck, and the cord would have been handmade and unique. Similarly, his staff was the staff of the patriarch of the tribe and would have been widely recognized. Ordinarily Judah would never have handed these over, but in this case he was so overconfident that this prostitute would give him his things back because they would have been basically useless to her that he gave them to her.
“and went in to her.” An idiom for sexual intercourse; the Hebrew is more literally “he went to her,” but it can also mean that he went “into” her, that is, he had sexual intercourse with her. This idiom occurs in a number of verses (cp. Gen. 29:23; 30:4; 38:2, 18; Judg. 16:1; Ruth 4:13; 2 Sam. 12:24).
“and she conceived by him.” This is one of the many times in Scripture that we see the invisible hand of God guiding history. It is normally unlikely that a woman gets pregnant by having sexual intercourse only once. Also, she herself would not have known it for at least a few weeks.