Semitic languages characteristically pair a plain consonant with an emphatic one, articulated further back in the mouth, and treat the two as separate sounds that separate words. Syriac inherits three such letters: teth beside taw, sadhe beside semkath, and qaph beside kaph. The distinctions were live when the alphabet was fixed and they are part of why the sequence has the shape it has.
Teth is the emphatic t. What exactly emphasis consisted of in the older languages is described differently in different accounts, since the evidence is spellings and later reading traditions rather than recordings, and the modern languages that keep the contrast do not all keep it the same way. In the classical reading of Syriac the letters are held apart, and spelling maintains the distinction regardless of how any particular community pronounces it.
The consequence for a reader is simple and practical. Two Syriac roots may differ only in whether they carry teth or taw, and nothing but the letter tells them apart. Unlike the dalath and rish pair, which share a shape, teth and taw look nothing alike, so this distinction survives even a badly written manuscript.
The emphatic letters also carry their own numeral values, teth nine and taw four hundred, and there the pairing does nothing at all. The numbering follows the order of the alphabet and takes no notice of which letters are related to which.