Tha is the aspirated voiceless dental, a t with breath released after it, and it holds the second slot of the dental class. It is not the th of English think, and it is not the th of English this. Sanskrit has neither of those sounds, and the two-letter Latin spelling used for this letter has misled readers of Sanskrit for as long as the convention has existed.
In Siddham the sound has a single character and no ambiguity. Aspiration belongs to the letter rather than to a mark added to another letter, so nothing about the written form invites the reading that the Latin spelling invites. That is a small but real argument for reading an Indian language in an Indian script, and it is one the East Asian tradition arrived at from the other direction: it kept the Siddham original precisely because its own transcriptions could not carry these distinctions.
The letter is reasonably common in the vocabulary and appears in several frequent grammatical formations. It takes the full range of vowel marks, carries the inherent short a, and enters conjuncts, most often with the semivowel ra and with the sibilants.
Its position in the class is predictable from the rule that governs all five, which puts the aspirate second in every group.